You are manager of a painting department of a large office complex. The painting

Question

You are manager of a painting department of a large office complex. The painting department is responsible for painting the buildings' exteriors and interiors. Your performance is judged in part on minimizing your department's operating costs, which consists of paint and labor, while providing a high-quality and timely service.

Your job of painting the halls of a particular building is being evaluated. Paint and labor are substitutes. To provide the quality job demanded you can use less paint and more labor, or more paint and less labor. The accompanying table summarizes this trade-off. Paint costs $10 per gallon, and labor costs $6.40 per hour.





Paint
(gallons)


Labor
(hours)




50


200




80


125




100


100




125


80




200


50



a. How much paint and how much labor do you choose in order to minimize the total cost of the hall paining job? (Show calculations in neatly labeled exhibit.)

b. The accounting department institutes an overhead allocation on labor. For every dollar spent on labor, $0.5625 of overhead is allocated to the paint department to cover corporate overhead items including payroll, human resources, security, legal costs, and so forth. Now how much labor and paint do you choose to minimize the total accounting cost of the hall painting job? (Show calculations in neatly labeled exhibit.)

c. Explain why your decisions differ between parts (a) and (b).

d. Explain why the accounting department might want to allocate corporate overhead based on direct labor to your painting department.

Explanation / Answer

A) the best option is option 2 with 80 gallons of paint and 125 hours of labor.

B) I would choose option 1 with 50 gallons of paint and 200 hours of labor.

Solving process:
To solve this I threw the numbers into an excel spreedsheet to make some quick calculations. Make a table with the options for paint and labor. Then multiply each unit by the cost. Then total the costs and compare the 5 options.
Ex: Paint (50*$10=$500), Labor (200*$6.40=$1280) $500+$1280=$1780 total cost.

The best option is the second with paint cost of $800 and labor of $800, totaling $1600.

Check figures: Option 3-$1640, 4-$1762, 5-$2320

Part B:
More overhead is allocated with more labor, which in turn would decrease the overall cost I believe. So I would think option 1 is the best choice. I'm not certain on part B, but part A option 2 is the best. 

 

My tables looked something like this.

Paint  $     10.00         Labor  $        6.40         Overhead  $        0.56                     Paint  $           50  $           80  $         100  $         125  $         200 Cost  $         500  $         800  $     1,000  $     1,250  $     2,000 Labor  $         200  $         125  $         100  $           80  $           50 Cost  $     1,280  $         800  $         640  $         512  $         320 Total  $     1,780  ***$1,600  $     1,640  $     1,762  $     2,320             Overhead  $         720  $         450  $         360  $         288  $         180 Paint less OH  $       (220)  $         350  $         640  $         962  $     1,820 New paint plus labor  ***$1,060  $     1,150  $     1,280  $     1,474  $     2,140

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