Problem 10-41 (Algorithmic) Sales mix with scarce resources San Fran Cycles manu

Question

Problem 10-41 (Algorithmic) Sales mix with scarce resources San Fran Cycles manually manufactures three unique bicycle models: racing, touring, and basic. All of the skilled craftspeople employed at San Fran can make each of the three models. Because it takes about a year to train each craftsperson, labor is a fixed production constraint over the short term. For 2013, the company expects to have available 38,700 labor hours. The average hourly labor rate is $31.

Data regarding the current product line follow.

The company pays taxes at the rate of 50 percent of operating income.

a. If an unlimited amount of any product can be sold, how many of each product should the company make? If an amount is zero, enter "0".

Racing

Touring

Basic

What pre-tax income will the company earn given your answer?

b. How many (rounded to the nearest whole unit) 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? Production levels:

Basic

Touring

Racing

What pre-tax income will the company earn given your answer?

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. The input in the box below will not be graded, but may be reviewed and considered by your instructor.

d. How does the company’s tax rate enter into the calculation of the optimal labor allocation? The input in the box below will not be graded, but may be reviewed and considered by your instructor.

Racing Touring Basic Selling price $ 3,615 $ 2,960 $ 1,023 Variable costs Direct material $ 865 $ 680 $ 240 Direct labor 1,550 1,240 310 Variable factory overhead 730 450 200 Variable selling 70 70 55 Fixed costs   Factory $ 377,000 Selling and administrative 82,000

Explanation / Answer

Maximize the contribution per unit of the scarce resource (direct labor hours):

                    Racing      Touring      Basic

            Sales per unit             $3615          $2960          $1023

            VC per unit                  (3215)         (2440)         (805)

            CM per unit                 $   400         $   520         $218

            Hours per bike                ÷50              ÷40            ÷ 10

            CM per hour                     $8            $13.00     $21.8.

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 or other restrictions. Profit can be determined as follows:

            Production of Basic cycles = 38700 ÷ 10 = 3870 (rounded)

     Contribution margin 3870 x $218           $843660

            Fixed costs                                                  (377000)

            Pretax income                                             $466660

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