Problem 10-41 Name:
Insert your answers into the gray-shaded cells. Enter amounts to be subtracted
as negatives. If an answer is incorrect, the word “wrong” will appear.
a. Maximizing the contribution margin per unit of scarce resource:
(Direct labor hours is the scarce resource)
Racing Touring Basic
Sales per unit 3,600$ 2,720$ 960$
VC per unit (3,180) (2,230) (744)
CM per unit 420$ 490$ 216$
Hours per bike 50 35 10
CM per hour 8.40 14.00 $21.60
If the company can sell an unlimited amount of any of the products, how many
of each product should it make?
What pre-tax income will the company earn given your answer?
Contribution margin 734,400$
Fixed costs (500,000)
Pretax income 234,400$
b. How many of each product must the company make if it has the policy to devote
no more than 50 percent of its available skilled labor capacity to any one product
but at least 20 percent to every product?
What pre-tax income will the company earn given your answer?
Production levels:
Total Labor Hrs. × Percentage ÷ Hours per Bike = Production
Basic 34,000 50% 10 1,700$ bikes
Racing 34,000 20% 50 136$ bikes
Touring 34,000 30% 35 291$ bikes
Solution
Since Basic cycles yield the greatest contribution margin per direct labor hour, the company
should devote all of its capacity to their production in the absence of market restrictions.
Profit can be determined as follows: Production of Basic cycles = 34,000 / 10 = 3,400
In part (a), it was determined that Basic cycles are the most profitable product, so the
company will devote 50 percent of its time to that product. Racing cycles yield the lowest
contribution margin per hour, so 20 percent of the time should be devoted to them. This
would leave 30 percent of the time to manufacture Touring cycles.
Contribution margin:
Production × CM per Unit
Basic 1,700 $216 367,200$
Racing 136 $420 57,120
Touring 291 $490 142,590
Total 566,910$
Less fixed costs (500,000)
Pretax income 66,910$
c. Given the nature of the three products, is it reasonable to believe that there are market
constraints on the mix of products that can be sold? Explain.
d. How does the company’s tax rate enter into the calculation of the optimal labor allocation?
Yes. The demand in this market is likely fragmented, with particular consumers perferring a
cycle suited for a particular purpose. However, there is likely enough demand for the Basic
cycle to absorb the entire production capacity of the company.
The company‘s tax rate is irrelevant because it does not change across the choices under
consideration in this decision.
bikes
bikes
bikes
Since Basic cycles yield the greatest contribution margin per direct labor hour, the company
should devote all of its capacity to their production in the absence of market restrictions.
Profit can be determined as follows: Production of Basic cycles = 34,000 / 10 = 3,400
In part (a), it was determined that Basic cycles are the most profitable product, so the
company will devote 50 percent of its time to that product. Racing cycles yield the lowest
contribution margin per hour, so 20 percent of the time should be devoted to them. This
would leave 30 percent of the time to manufacture Touring cycles.
Given the nature of the three products, is it reasonable to believe that there are market
How does the company‘s tax rate enter into the calculation of the optimal labor allocation?
Yes. The demand in this market is likely fragmented, with particular consumers perferring a
cycle suited for a particular purpose. However, there is likely enough demand for the Basic
cycle to absorb the entire production capacity of the company.
The company‘s tax rate is irrelevant because it does not change across the choices under
consideration in this decision.