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.