a The Witchell Corporation manufactures and sells three grades A, B, and C, of a single wood product. Each grade must be processed through three phases—cutting, fitting, and finishing—

before it is sold.

The following unit information is provided: 1475

Required:
Formulate and label the linear objective function and the constraint functions necessary to maximize the total contribution margin.
b The graph provided on page 826 presents the constraint functions for a chair manufacturing company whose production problem can be solved by linear programming. The company earns $8.00 for each kitchen chair sold and $5.00 for each office chair sold.
Required:
1 What is the profit-maximizing production schedule?
2 How did you select this production schedule?

Transcribed Image Text:

A B C Selling price Direct labor $10.00 $15.00 $20.00 $ 5.00 $ 6.00 $ 9.00 Direct materials $ .70 $ .70 $ 1.00 Variable overhead $ 1.00 $ 1.20 $ 1.80 Fixed overhead $ .60 $ .72 $ 1.08 Materials requirements in board feet 7 7 10 Labor requirements in hours Cutting Fitting Finishing Only 5,000 board feet per week can be obtained. The Cutting Department has 180 hours of labor available each week. The Fitting and Finishing Departments each have 120 hours of labor available each week. No overtime is allowed. Contract commitments require the company to make 50 units of A per week. In addition. company policy is to produce at least 50 additional units of A and 50 units of B and 50 units of C each week to actively remain in each of the three markets. Because of competition only 130 units of C can be sold each week.