if the company can sell an unlimited amount of any of the products how many of each 643187

(Sales mix with scarce resources) San Fran Cycles manually manufactures three unique bicycle models: racing, touring, and basic. All of the skilled crafts people 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 2010, the company expects to have available 34,000 labor hours. The average hourly labor rate is $30. Data regarding the current product line follow.

		Racing	Touring	Basic
Selling price		$3,600	$2,720	$960
Variable costs
Direct material		$ 880	$ 640	$240
Direct labor		1,500	1,050	300
Variable factory overhead		720	480	164
Variable selling		80	60	40
Fixed costs
Factory	$400,000
Selling and administrative	100,000

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

a. 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?

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?

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?