(Sales mix with scarce resources) EuroCycles makes wholly by hand three unique bicycle models: racing, touring, and basic. All products are made by skilled craftspeople experienced in making all three models. Because it takes about a year to train each craftsperson, labor is a fixed production constraint over the short term. For 2006, the company expects to have available 34,000 labor hours. The average hourly labor rate is $25. Data regarding the current product line follow:

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 opti¬ mal labor allocation?

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Racing Touring Basic Selling price Variable costs Direct material Direct labor Variable factory overhead $1,800 $1,360 $480 $440 $320 $120 600 550 150 360 240 82 Variable selling 40 30 20 Fixed costs Factory $300,000 Selling and administrative 150,000