Problem:
(Sales mix with scarce resources) Hartford Furniture makes three unique wood
products: desks, chairs, and footstools. These products are made wholly by hand; no electric or hydraulic machinery is used in production. All products are made by skilled craftspeople who have been trained to make all three products. Because it takes about a year to train each craftsperson, labor is a fixed production constraint over the short term. For 2002, the company expects to have available 34,000 labor hours. The average hourly labor rate is $25. Data regarding the current product line follow:
|
Desks
|
Chairs
|
Footstools
|
|
Selling price
|
$900
|
$680
|
$240
|
|
Variable costs:
|
|
Direct material
|
$220
|
$160
|
$ 60
|
|
Direct labor
|
300
|
275
|
75
|
|
Variable factory overhead
|
180
|
120
|
41
|
|
Variable selling
|
20
|
15
|
10
|
|
Fixed costs:
|
|
Factory
|
|
$150,000
|
|
|
Selling & administrative
|
75,000
|
|
The company is in the 50 percent tax bracket.
a. If the company can sell an unlimited amount of any of the products, how many of each product should it make? What pretax income will the company earn given your answer?
b. How many of each product must the company make if it has a policy of devoting no more than 50 percent of its available skilled labor capacity to any one product and at least 20 percent to every product? What pretax in come 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