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Problems

1. A bank has a drive-in window, which is open from 10 a.m. to 3 p.m. on business days. Customers drive up at a mean rate of 12 per hour, according to a Poisson distribution. The teller requires a mean of 2.4 minutes to serve each customer. service times have a negative exponential distribution.

  1. How many channels are there?
  2. Do the customers come from a finite source or from an infinite source?
  3. Which queue model is appropriate here?
  4. What is the value of <a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=gif::Image306::/sites/dl/free/0072443901/24520/Image306.gif','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif">Image306 (0.0K)</a>Image306 ?
  5. What is the interpretation of <a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=gif::Image306::/sites/dl/free/0072443901/24520/Image306.gif','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif">Image306 (0.0K)</a>Image306 ?
  6. What is the value of <a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=gif::Image307::/sites/dl/free/0072443901/24520/Image307.gif','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif">Image307 (0.0K)</a>Image307 ?
  7. What is the interpretation of <a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=gif::Image307::/sites/dl/free/0072443901/24520/Image307.gif','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif">Image307 (0.0K)</a>Image307 ?
  8. What is the system utilization, <a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=gif::Image308::/sites/dl/free/0072443901/24520/Image308.gif','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif">Image308 (0.0K)</a>Image308 ? Is this a feasible system?
  9. What is the proportion of idle time?
  10. What is the mean number of customers being served?
  11. What is the expected number of customers waiting for service?
  12. What is the expected duration of the wait?
  13. What is the mean number of customers in the system?
  14. What is the mean time that a customer spends in the system?
  15. What is the probability that the system will be idle?
  16. What is the probability that there will be one car in the system?
  17. What is the probability that there will be three cars in the system?

2. In a factory, the parts to be copper-plated must be immersed in an electrolytic solution so that copper ions will be deposited on the part. The company has one electrolytic bath, in which each part is submerged for 20 minutes. Parts to be copper-plated arrive at a mean rate of 20 per 8-hour shift, according to a Poisson distribution.

  1. How many channels are there?
  2. Do the parts come from a finite source or from an infinite source?
  3. Which queue model is appropriate here?
  4. What is the value of <a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=gif::Image306::/sites/dl/free/0072443901/24520/Image306.gif','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif">Image306 (0.0K)</a>Image306 ?
  5. What is the interpretation of <a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=gif::Image306::/sites/dl/free/0072443901/24520/Image306.gif','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif">Image306 (0.0K)</a>Image306 ?
  6. What is the value of <a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=gif::Image307::/sites/dl/free/0072443901/24520/Image307.gif','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif">Image307 (0.0K)</a>Image307 ?
  7. What is the interpretation of <a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=gif::Image307::/sites/dl/free/0072443901/24520/Image307.gif','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif">Image307 (0.0K)</a>Image307 ?
  8. What is the system utilization, <a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=gif::Image309::/sites/dl/free/0072443901/24520/Image309.gif','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif">Image309 (0.0K)</a>Image309 ? Is this a feasible system?
  9. What is the proportion of idle time?
  10. What is the expected number of parts waiting for copper-plating?
  11. What is the expected duration of the wait?
  12. What is the mean number of parts in the system?
  13. What is the mean time that a part spends in the system?

3. A bank has an array of five drive-in windows, some or all of which may be open from 10 a.m. to 3 p.m. on normal business days. At each window, the teller requires a mean of 2.4 minutes to serve each customer; service times have a negative exponential distribution. Customers arrive at a mean rate of 65 per hour, according to a Poisson distribution. (Use Table 19-4)

  1. Do the customers come from a finite source or from an infinite source?
  2. What is the value of <a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=gif::Image306::/sites/dl/free/0072443901/24520/Image306.gif','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif">Image306 (0.0K)</a>Image306 ?
  3. What is the interpretation of <a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=gif::Image306::/sites/dl/free/0072443901/24520/Image306.gif','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif">Image306 (0.0K)</a>Image306 ?
  4. What is the value of <a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=gif::Image307::/sites/dl/free/0072443901/24520/Image307.gif','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif">Image307 (0.0K)</a>Image307 ?
  5. What is the interpretation of <a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=gif::Image307::/sites/dl/free/0072443901/24520/Image307.gif','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif">Image307 (0.0K)</a>Image307 ?
  6. What is the minimum number of drive-in windows which should be open to have an underloaded system?
  7. What is the expected number of customers waiting for service with three drive-in windows open?
  8. What is the expected duration of the wait?
  9. What is the expected duration of the wait if all three open windows are busy.?
  10. What is the probability that the system will be idle?
  11. What is the probability that an arrival will have to wait for service?

4. Rework Problem 3 with five drive-in windows open.

  1. What is the expected number of customers waiting for service?
  2. What is the expected duration of the wait?
  3. What is the expected duration of the wait if all five windows are busy?
  4. What is the probability that the system will be idle?
  5. hat is the probability that an arrival will have to wait for service?

5. The bus company in a small city has a fleet of 10 buses and a single mechanic to service the buses as needed. Buses break down or require periodic maintenance at a mean rate of one every other day, seven days a week. The mechanic works five days per week (40 hours), and the mean time required to service one bus is four hours, with a negative exponential distribution. Buses which break down on Saturday or Sunday are parked until the mechanic can attend to them in the following week.

  1. How many channels are there?
  2. Should the bus arrivals be treated as coming from a finite source or from an infinite source?
  3. Which waiting line model is appropriate here?
  4. What is the number of potential customers, N?
  5. What is the value of the mean service time, T?
  6. What is the value of the mean time between service calls, U?
  7. What is the value of the service factor, X?
  8. What is the value of the efficiency factor, F?
  9. What is the expected number of buses running, J?
  10. What is the mean number of buses being serviced, H?
  11. What is the mean number of buses waiting for the mechanic, L?
    1. Check to see that N = J + L + H.

    12. 6. A typing pool for a large corporation consists of six typists, each of whom can type at the rate of 12 pages per hour, on the average, with a Poisson distribution. The pool receives various kinds of typing jobs from a very large number of executives and managers. The jobs are classified into four priority levels as they arrive. Each level is shown below, with the mean of its particular arrival rate. Typing jobs arrive according to Poisson distributions:

    first priority: correspondence with customers (to be typed first); <a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=gif::Image310 ::/sites/dl/free/0072443901/24520/Image310.gif','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif">Image310 (0.0K)</a>Image310 pages per hr.
    second priority: correspondence with suppliers; <a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=gif::Image311::/sites/dl/free/0072443901/24520/Image311.gif','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif">Image311 (0.0K)</a>Image311 pages per hr.
    third priority: correspondence with federal, state, and local governments (other than that dealing with sales);<a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=gif::Image312::/sites/dl/free/0072443901/24520/Image312.gif','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif">Image312 (0.0K)</a>Image312 pages per hr.
    fourth priority: internal memoranda and communications and miscellaneous correspondence; <a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=gif::Image313::/sites/dl/free/0072443901/24520/Image313.gif','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif">Image313 (0.0K)</a>Image313 pages per hr.

    1. Which set of waiting line formulas should be used here?
    2. What is s?
    3. What is the value of <a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=gif::Image314::/sites/dl/free/0072443901/24520/Image314.gif','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif">Image314 (0.0K)</a>Image314 ?
    4. What is <a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=gif::Image315::/sites/dl/free/0072443901/24520/Image315.gif','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif">Image315 (0.0K)</a>Image315 ?
    5. What is the value of <a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=gif::Image307::/sites/dl/free/0072443901/24520/Image307.gif','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif">Image307 (0.0K)</a>Image307 ?
    6. What is <a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=gif::Image316::/sites/dl/free/0072443901/24520/Image316.gif','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif">Image316 (0.0K)</a>Image316 ?
    7. What is the system utilization, <a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=gif::Image317::/sites/dl/free/0072443901/24520/Image317.gif','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif">Image317 (0.0K)</a>Image317 ?
    8. On the average, how many pages are being typed at any one time?
    9. Determine the value of <a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=gif::Image318::/sites/dl/free/0072443901/24520/Image318.gif','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif">Image318 (0.0K)</a>Image318 ?
    10. Determine the value of A
    11. Determine these values:
      <a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=gif::Image319::/sites/dl/free/0072443901/24520/Image319.gif','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif">Image319 (0.0K)</a>Image319
      <a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=gif::Image320::/sites/dl/free/0072443901/24520/Image320.gif','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif">Image320 (0.0K)</a>Image320
      <a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=gif::Image321::/sites/dl/free/0072443901/24520/Image321.gif','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif">Image321 (0.0K)</a>Image321
      <a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=gif::Image322::/sites/dl/free/0072443901/24520/Image322.gif','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif">Image322 (0.0K)</a>Image322
      <a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=gif::Image323::/sites/dl/free/0072443901/24520/Image323.gif','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif">Image323 (0.0K)</a>Image323
    12. Determine these values:
      <a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=gif::Image324::/sites/dl/free/0072443901/24520/Image324.gif','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif">Image324 (0.0K)</a>Image324
      <a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=gif::Image325::/sites/dl/free/0072443901/24520/Image325.gif','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif">Image325 (0.0K)</a>Image325
      <a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=gif::Image326::/sites/dl/free/0072443901/24520/Image326.gif','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif">Image326 (0.0K)</a>Image326
      <a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=gif::Image327::/sites/dl/free/0072443901/24520/Image327.gif','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif">Image327 (0.0K)</a>Image327
    13. Find the average time in the system for pages in each priority class.
    14. Find the average number of pages in the queue for each priority class.
    15. Discuss the results of the above analysis.

    7. Refer to problem #1.

    1. What line length will not be exceeded 95% of the time?
    2. Refer to problem #3. What line length will not be exceeded 98% of the time?

     

     

    Solutions

    1. a. M = 1 channel.
    b. An infinite source.
    c. Single channel, single phase, Poisson arrivals, negative exponential service times.
    d. <a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=gif::Image328::/sites/dl/free/0072443901/24520/Image328.gif','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif">Image328 (0.0K)</a>Image328 cars per hour.
    e. <a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=gif::Image314::/sites/dl/free/0072443901/24520/Image314.gif','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif">Image314 (0.0K)</a>Image314 is the mean number of customers who demand service every hour.
    f. <a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=gif::Image329::/sites/dl/free/0072443901/24520/Image329.gif','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif">Image329 (0.0K)</a>Image329 minutes and cars per hour.
    g. <a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=gif::Image307::/sites/dl/free/0072443901/24520/Image307.gif','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif">Image307 (0.0K)</a>Image307 is the mean number of cars which the teller can handle in one hour.
    h. <a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=gif::Image331::/sites/dl/free/0072443901/24520/Image331.gif','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif">Image331 (1.0K)</a>Image331 , which is less than 1. The system is feasible.
    i. The proportion of idle time = <a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=gif::Image332::/sites/dl/free/0072443901/24520/Image332.gif','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif">Image332 (1.0K)</a>Image332
    j. <a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=gif::Image333::/sites/dl/free/0072443901/24520/Image333.gif','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif">Image333 (1.0K)</a>Image333 customers.
    k. <a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=gif::Image334::/sites/dl/free/0072443901/24520/Image334.gif','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif">Image334 (1.0K)</a>Image334 cars in the queue.
    l. <a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=gif::Image335::/sites/dl/free/0072443901/24520/Image335.gif','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif">Image335 (1.0K)</a>Image335 hrs. or 2.20 min.
    m. <a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=gif::Image336::/sites/dl/free/0072443901/24520/Image336.gif','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif">Image336 (1.0K)</a>Image336 cars.
    n. <a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=gif::Image337::/sites/dl/free/0072443901/24520/Image337.gif','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif">Image337 (1.0K)</a>Image337 min.
    o. p(0 cars) <a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=gif::Image338::/sites/dl/free/0072443901/24520/Image338.gif','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif">Image338 (1.0K)</a>Image338 .
    p. p(1 car) <a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=gif::Image339::/sites/dl/free/0072443901/24520/Image339.gif','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif">Image339 (1.0K)</a>Image339 .
    q. p(3 cars) <a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=gif::Image340::/sites/dl/free/0072443901/24520/Image340.gif','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif">Image340 (1.0K)</a>Image340

      .

       

      2. a. M = 1 channel.
      b. An infinite population.
      c. Single channel, single phase, Poisson arrivals, constant service times.
      d. <a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=gif::Image341::/sites/dl/free/0072443901/24520/Image341.gif','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif">Image341 (0.0K)</a>Image341 parts per shift or 2 per hour.
      e. <a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=gif::Image342::/sites/dl/free/0072443901/24520/Image342.gif','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif">Image342 (0.0K)</a>Image342 is the mean number of parts which arrive per time period.
      f. <a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=gif::Image343::/sites/dl/free/0072443901/24520/Image343.gif','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif">Image343 (0.0K)</a>Image343 min. and <a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=gif::Image344::/sites/dl/free/0072443901/24520/Image344.gif','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif">Image344 (1.0K)</a>Image344 parts per shift.
      g. <a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=gif::Image307::/sites/dl/free/0072443901/24520/Image307.gif','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif">Image307 (0.0K)</a>Image307 is the maximum number of pieces which can be electro-plated per shift. (Compare this with 1-g.)
      h. <a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=gif::Image345 ::/sites/dl/free/0072443901/24520/Image345.gif','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif">Image345 (1.0K)</a>Image345 . The electrolytic bath is in use 67% of the time and system is feasible.
      i. The proportion of idle time <a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=gif::Image346::/sites/dl/free/0072443901/24520/Image346.gif','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif">Image346 (1.0K)</a>Image346
      j. <a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=gif::Image347::/sites/dl/free/0072443901/24520/Image347.gif','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif">Image347 (1.0K)</a>Image347 .
      k. <a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=gif::Image348::/sites/dl/free/0072443901/24520/Image348.gif','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif">Image348 (1.0K)</a>Image348 parts.
      l. <a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=gif::Image349::/sites/dl/free/0072443901/24520/Image349.gif','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif">Image349 (1.0K)</a>Image349 .of an 8-hour shift, or .0417(8) = .3333 hrs. or 20 minutes.
      m. <a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=gif::Image350::/sites/dl/free/0072443901/24520/Image350.gif','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif">Image350 (1.0K)</a>Image350 parts.
      n. <a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=gif::Image351::/sites/dl/free/0072443901/24520/Image351.gif','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif">Image351 (1.0K)</a>Image351 min.

       

      3. a. An infinite source.
      b. <a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=gif::Image352::/sites/dl/free/0072443901/24520/Image352.gif','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif">Image352 (0.0K)</a>Image352 customers per hr.
      c. <a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=gif::Image314::/sites/dl/free/0072443901/24520/Image314.gif','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif">Image314 (0.0K)</a>Image314 is the mean number of customers who demand service at the array of drive-in windows per hour.
      d. At each window, <a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=gif::Image353::/sites/dl/free/0072443901/24520/Image353.gif','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif">Image353 (0.0K)</a>Image353 min. and <a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=gif::Image354::/sites/dl/free/0072443901/24520/Image354.gif','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif">Image354 (0.0K)</a>Image354 customers per hr.
      e. <a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=gif::Image307::/sites/dl/free/0072443901/24520/Image307.gif','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif">Image307 (0.0K)</a>Image307 is the mean number of customers which any one teller can handle in one hour.
      f. <a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=gif::Image309::/sites/dl/free/0072443901/24520/Image309.gif','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif">Image309 (0.0K)</a>Image309 must be less than 1; hence <a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=gif::Image355::/sites/dl/free/0072443901/24520/Image355.gif','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif">Image355 (1.0K)</a>Image355 and M must be at least 3.
      g. Use Table 19-4 in your textbook. <a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=gif::Image356::/sites/dl/free/0072443901/24520/Image356.gif','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif">Image356 (1.0K)</a>Image356 and <a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=gif::Image357::/sites/dl/free/0072443901/24520/Image357.gif','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif">Image357 (0.0K)</a>Image357 cars.
      h. <a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=gif::Image358::/sites/dl/free/0072443901/24520/Image358.gif','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif">Image358 (1.0K)</a>Image358 hrs. = 4.55 min.
      i. <a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=gif::Image359::/sites/dl/free/0072443901/24520/Image359.gif','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif">Image359 (1.0K)</a>Image359 hrs. = 6 min.
      j. Use table 19-4; p(0) = .035.
      k.
      l. <a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=gif::Image360::/sites/dl/free/0072443901/24520/Image360.gif','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif">Image360 (1.0K)</a>Image360

      4. a. Use Table 19-4; <a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=gif::Image361::/sites/dl/free/0072443901/24520/Image361.gif','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif">Image361 (1.0K)</a>Image361 and <a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=gif::Image362::/sites/dl/free/0072443901/24520/Image362.gif','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif">Image362 (0.0K)</a>Image362 cars.
      b. <a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=gif::Image363::/sites/dl/free/0072443901/24520/Image363.gif','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif">Image363 (1.0K)</a>Image363 hrs. = 8.9 sec.
      c. <a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=gif::Image364::/sites/dl/free/0072443901/24520/Image364.gif','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif">Image364 (1.0K)</a>Image364 hrs. = 60.1 sec.
      d. Use Table 19-4; p(0) = .072.
      e. <a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=gif::Image365::/sites/dl/free/0072443901/24520/Image365.gif','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif">Image365 (1.0K)</a>Image365

        .

        5. a. M = 1 channel, namely the mechanic.
        b. The customers come from the finite fleet of 10 buses.
        c. The finite source model.
        d. N = 10 buses.
        e. T = 4 hrs.
        f. Presumably the buses run 24 hours a day, 7 days a week. U = 168 hrs./3.5 breakdowns = 48 hrs. between breakdowns.
        g. X = T/(T + U) = 4/(4 + 48) = .077.
        h. Use table 19-7 in your textbook. For X = .077 and M = 1, F » .973.
        i. J = N(F)(1 - X) = 10(.973)(1 - .077) = 8.98 buses.
        j. H = F(N)(X) = .973(10)(.077) = .75 buses.
        k. L = N(1 - F) = 10(1 - .973) = .27 buses.
        l. Check: N = J + L + K = 8.98 + .75 + .27 = 10 buses.<a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=gif::Image366::/sites/dl/free/0072443901/24520/Image366.gif','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif">Image366 (0.0K)</a>Image366

         

        6. a. The multiple-channel, multiple-priority model.
        b. s = 6 typists.
        c. <a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=gif::Image367::/sites/dl/free/0072443901/24520/Image367.gif','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif">Image367 (1.0K)</a>Image367 pages per hr.
        d. <a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=gif::Image368::/sites/dl/free/0072443901/24520/Image368.gif','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif">Image368 (1.0K)</a>Image368 hrs =66.67 sec.
        e. <a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=gif::Image369::/sites/dl/free/0072443901/24520/Image369.gif','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif">Image369 (0.0K)</a>Image369 pages per hr.
        f. <a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=gif::Image370::/sites/dl/free/0072443901/24520/Image370.gif','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif">Image370 (0.0K)</a>Image370 hrs. = 5 min.
        g. <a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=gif::Image371::/sites/dl/free/0072443901/24520/Image371.gif','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif">Image371 (1.0K)</a>Image371 .
        h. <a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=gif::Image372::/sites/dl/free/0072443901/24520/Image372.gif','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif">Image372 (1.0K)</a>Image372 pages.
        i. <a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=gif::Image373::/sites/dl/free/0072443901/24520/Image373.gif','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif">Image373 (0.0K)</a>Image373 customers (from Table 19-4).
        j. <a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=gif::Image374::/sites/dl/free/0072443901/24520/Image374.gif','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif">Image374 (1.0K)</a>Image374 .
        k. <a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=gif::Image375::/sites/dl/free/0072443901/24520/Image375.gif','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif">Image375 (0.0K)</a>Image375
        <a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=gif::Image376::/sites/dl/free/0072443901/24520/Image376.gif','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif">Image376 (1.0K)</a>Image376
        <a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=gif::Image377::/sites/dl/free/0072443901/24520/Image377.gif','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif">Image377 (1.0K)</a>Image377
        <a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=gif::Image378::/sites/dl/free/0072443901/24520/Image378.gif','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif">Image378 (1.0K)</a>Image378
        . <a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=gif::Image379::/sites/dl/free/0072443901/24520/Image379.gif','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif">Image379 (1.0K)</a>Image379
        l. <a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=gif::Image380::/sites/dl/free/0072443901/24520/Image380.gif','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif">Image380 (1.0K)</a>Image380 hrs. = 24 sec.
        <a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=gif::Image381::/sites/dl/free/0072443901/24520/Image381.gif','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif">Image381 (1.0K)</a>Image381 hrs. = 32 sec.
        <a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=gif::Image382::/sites/dl/free/0072443901/24520/Image382.gif','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif">Image382 (1.0K)</a>Image382 hrs. = 40 sec.
        <a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=gif::Image383::/sites/dl/free/0072443901/24520/Image383.gif','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif">Image383 (1.0K)</a>Image383 hrs. = 2.1 min.
        m. Priority

      ClassAverage Time in System
      1<a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=gif::Image384::/sites/dl/free/0072443901/24520/Image384.gif','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif">Image384 (1.0K)</a>Image384 min
      2<a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=gif::Image385::/sites/dl/free/0072443901/24520/Image385.gif','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif">Image385 (1.0K)</a>Image385 min
      3<a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=gif::Image386::/sites/dl/free/0072443901/24520/Image386.gif','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif">Image386 (1.0K)</a>Image386 min
      4<a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=gif::Image387::/sites/dl/free/0072443901/24520/Image387.gif','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif">Image387 (1.0K)</a>Image387 min

      n. Priority

      Class Average Pages in Queue
      1<a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=gif::Image388::/sites/dl/free/0072443901/24520/Image388.gif','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif">Image388 (1.0K)</a>Image388 pages
      2<a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=gif::Image389::/sites/dl/free/0072443901/24520/Image389.gif','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif">Image389 (1.0K)</a>Image389 pages
      3<a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=gif::Image390::/sites/dl/free/0072443901/24520/Image390.gif','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif">Image390 (1.0K)</a>Image390 pages
      4<a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=gif::Image391::/sites/dl/free/0072443901/24520/Image391.gif','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif">Image391 (1.0K)</a>Image391 pages

      o. This system looks feasible; <a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=gif::Image392::/sites/dl/free/0072443901/24520/Image392.gif','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif">Image392 (0.0K)</a>Image392 and the jobs in each priority class are typed within a reasonable time, on the average.

         

        7. a. <a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=gif::Image393::/sites/dl/free/0072443901/24520/Image393.gif','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif">Image393 (1.0K)</a>Image393
        ln K = ln 0.2185 = -1.52
        ln = ln 0.48 = -0.73
        number of customers = <a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=gif::Image395::/sites/dl/free/0072443901/24520/Image395.gif','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif">Image395 (1.0K)</a>Image395

        b. <a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=gif::Image396::/sites/dl/free/0072443901/24520/Image396.gif','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif">Image396 (1.0K)</a>Image396
        ln K = ln 0.030 = -3.506
        ln <a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=gif::Image394::/sites/dl/free/0072443901/24520/Image394.gif','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif">Image394 (0.0K)</a>Image394 = ln 0.867 = -0.143
        number of customers = n = ln K/ln <a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=gif::Image394::/sites/dl/free/0072443901/24520/Image394.gif','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif">Image394 (0.0K)</a>Image394 = -3.506/-0.143 = 24.52 <a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=gif::Image120::/sites/dl/free/0072443901/24520/Image120.gif','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif">Image120 (0.0K)</a>Image120 25.00.

         






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