Problems

1. Solve the following exercises by referring to Table 7S- I in your textbook.

1. In the production of cargo planes, an 80 percent learning curve is experienced. It takes 2,000 direct labor hours to produce the first plane. Estimate the direct labor hours required to produce the 10th plane.
2. In the above case, estimate the total direct labor hours required to produce the first 10 planes.
3. In the construction of tract houses, a 90 percent learning curve is experienced. It takes 3,000 direct labor hours to construct the first house. Estimate the direct labor hours required to construct the 15th house.
4. In the above case, estimate the total direct labor hours required to construct the first 6 houses.

2. The Emperor Shipyards Co. has a contract to build 20 identical oil tankers. The production manager believes that an 85 percent learning curve is appropriate for direct labor time. The wages of the workers average $12.00 per hour, with fringe benefits of 30 percent. The following accounting data have been accumulated on the first tanker.

Direct labor 25,000 hr.
Direct materials $200,000

1. What is the interpretation of the 85 percent?
2. Estimate the direct labor time required to build the 5th tanker.
3. Estimate the total direct cost of the 5th tanker.
4. Estimate the total direct labor time required to build all 20 tankers.
5. Estimate the total direct cost of all 20 tankers.
6. Find the price per tanker which is 150 percent higher than the total direct cost per tanker.

3. The formula for the learning curve is: <a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=gif::Image218::/sites/dl/free/0072443901/24520/Image218.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">Image218 (0.0K)</a>Image218 , where:

T_n = time f or the nth unit
T₁ = time for the first unit
b = ln(learning percent)/ln 2

Use the <a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=gif::Image219::/sites/dl/free/0072443901/24520/Image219.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">Image219 (0.0K)</a>Image219 key or the lnx key on your calculator to solve these problems:

1. ln 2 = ?
2. Learning percent = 85%, Ln(learning percent) = ?
3. b = ?
4. T₁ = 5, 000 hrs. T₄ = ?

4. Use the formulas in problem #3 to solve these problems:

1. Learning percent = 82%, Ln(learning percent) = ?
2. b = ?
3. T₁ = 7, 000 hrs. T₅ = ?

Solutions

1. a. .477(2000) = 954 direct labor hours.
b. 6.315(2000) = 12,630 direct labor hours.
c. .663(3000) = 1,989 direct labor hours.
d. 5.101(3000) = 15,303 direct labor hours.

2. a. Every time the output doubles, the time required to produce one unit is 85% as large as it was before the doubling occurred.
b. .686(25000) = 17,150 direct labor hours.
c. Direct Labor) 17,150 hrs.($12.00) = $205,800.00
Fringe Benefits) 205,800.00(.30) = 61,740.00
Direct Materials) 200,000.00
Total $467,540.00
d. 12.402(25000) = 310,050 direct labor hours.
e. Direct Labor) 310,050 hrs.($12.00) = $3,720,600.00
Fringe Benefits) 3,720,600(.30) = 1,116,180.00
Direct Materials) 20($200,000) = 4,000,000.00
Total Cost $8,836,780.00
f. The mean direct cost per tanker is estimated at 8,836,780/20 » $441,839.00. The price per tanker would be 441,839 x (2.50) = $1,104,598.00.

3. a. Ln 2 = 0.6931.
b. Ln .85 = -0.1625.
c. b = Ln .85/Ln 2 = -0.1625/0.6931 = -0.2345.
d. <a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=gif::Image220::/sites/dl/free/0072443901/24520/Image220.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">Image220 (1.0K)</a>Image220 hrs.

4. a. Ln .82 = -0.1985.
b. b = Ln .82/Ln 2 = -0.1985/0.6931 = -0.2863.
c. <a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=gif::Image221::/sites/dl/free/0072443901/24520/Image221.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">Image221 (1.0K)</a>Image221 hrs.