Problems

1. Two plant locations are under consideration for a new battery factory. Here are estimates of the fixed and variable costs at each location.

Location Fixed Cost per Year Variable Cost per Unit

A $1,500,000 $1.25
B 1,250,000 1.75

1. What is the total cost function for each location?
2. Plot the total cost functions on the same graph.
3. On the graph, identify the range of output for which each location has the least cost.
4. Which location should be selected for an output of 400,000 batteries per year? 800,000 batteries per year?
5. Find the cutoff point algebraically.

2. Four plant locations arc under consideration for a new microchip plant. Here are estimates of the fixed and variable costs at each location.

1. What is the total cost function for each location?
2. Plot the total cost functions for these locations on the same graph.
3. On the graph, identify the range of output for which each location has the least cost.
4. Which location should be selected for an output of 4,000 chips per year? 12,000 chips per year?
5. Find the cutoff points algebraically.

3. Two locations are under consideration for building a condominium. (A condominium is a building in which each apartment is owned by the resident, rather than rented.) One location is in suburb A of a large Eastern city, and the other is in suburb B. The marketing manager has identified the following factors which bear upon the location decision and their relative weights.

Each factor will be rated on a scale of 1 = unsatisfactory to 10 = outstanding. Research has revealed the following information about each location, and the marketing manager has rated each factor at each location.

1. Construct a rating analysis worksheet in the style of Example 2 in your textbook and determine the composite score for each location.
2. Where should the condominium be built? Why?

4. Business has been good for the Black & White News Company, which receives magazines from the publishers and distributes them to the news racks of drugstores and supermarkets. At present, it has five customers, each of which is serviced once a week; expired magazines are collected and new editions are displayed on the racks. (This problem is obviously artificially small.) Here are the x and y coordinates of the locations of the customers and the number of truckloads of magazines which go to each destination. The company operates out of a single warehouse, whose coordinates are also included. The company has outgrown the warehouse, and the partners are discussing whether to expand the present facilities or to construct a larger warehouse at a new site.

1. Plot the locations of the customers on graph paper.
2. What is the mean of x?
3. What is the mean of y?
4. Plot the optimal location of the warehouse on your graph.
5. Based solely on this analysis, should the partners enlarge the present warehouse or construct a new one?

Solutions
1. a. A)<a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=gif::Image222::/sites/dl/free/0072443901/24520/Image222.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">Image222 (1.0K)</a>Image222
B) <a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=gif::Image223::/sites/dl/free/0072443901/24520/Image223.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">Image223 (1.0K)</a>Image223
b, c.
d. For 400,000 batteries, location B is less expensive. For 800,000 batteries, location A is less expensive.
e. At the cutoff point (Q), the total costs will be equal at both locations.
<a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=gif::Image224::/sites/dl/free/0072443901/24520/Image224.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">Image224 (0.0K)</a>Image224
1,500,000 + 1.25Q = 1,250,000 + 1.75Q
Q = 500,000 batteries.

2. a. A)<a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=gif::Image225::/sites/dl/free/0072443901/24520/Image225.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">Image225 (1.0K)</a>Image225

B) <a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=gif::Image226::/sites/dl/free/0072443901/24520/Image226.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">Image226 (1.0K)</a>Image226
C) <a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=gif::Image227::/sites/dl/free/0072443901/24520/Image227.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">Image227 (1.0K)</a>Image227
D) <a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=gif::Image228::/sites/dl/free/0072443901/24520/Image228.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">Image228 (1.0K)</a>Image228
b, c.
d. For 4,000 chips, location A is the least expensive. For 12,000 chips, location D is the least expensive.
e. <a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=gif::Image229::/sites/dl/free/0072443901/24520/Image229.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">Image229 (0.0K)</a>Image229
3,000,000 + 800Q = 3,500,000 + 600Q
Q = 2,500 microchips. 

At a lower volume, B is superior; at a higher volume, A is superior. The cutoff point between A and C is 5,000 microchips. The cutoff point between C and D is 10,000 microchips.


3. a.

4. a.

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b.<a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=gif::Image230::/sites/dl/free/0072443901/24520/Image230.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">Image230 (1.0K)</a>Image230 .
c. <a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=gif::Image231::/sites/dl/free/0072443901/24520/Image231.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">Image231 (1.0K)</a>Image231
d.
e. The partners should build a new warehouse at <a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=gif::Image232 ::/sites/dl/free/0072443901/24520/Image232.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">Image232 (0.0K)</a>Image232 and <a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=gif::Image233::/sites/dl/free/0072443901/24520/Image233.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">Image233 (0.0K)</a>Image233 , since shipping expenses should be lower from the new warehouse.