A company’s top management is seeking ways to improve the profitability of one of its newer plants. The president asked the director of internal auditing to review that plant’s product-mix decisions to assist management in meeting its objective of improved profitability. The internal auditor assigned to the review developed the following data:

1. Monthly profit data by product line:

2. Demand for each of the plant’s three products is so great that the plant can easily sell whatever quantity of each product it produces. The internal auditor constructed the following LP (linear programming) model of the plant’s operation:

3. Slack variables x4 and x5 were added to constraints 1 and 2, respectively, and the optimal tableau shown on the next page was generated by a computer program:
Required:
Analyze the information given and provide answers to the following questions:

a. How many units of xj and x3 should be produced, and what would be their total contribution margin?

b. How many units of x72 should be produced? Explain your answer.

c. Why is linear programming the appropriate technique to employ in the situation above?

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Product X1 X2 X3 Total Hours Available Sales Variable costs $3,750 $3,000 $6,000 $1,200 $1,350 $2,250 Fixed costs Operating profit $2,625 $1,050 $3,675 $ (75) $ 600 $ 75 Net contribution per unit Monthly production (units) Unit selling price Unit variable cost Labor hours per unit: Department 1 Department 2 150 50 150 $ 25 $ 60 $ 40 $ 8 $ 27 $ 15 $ 17 $ 33 $ 25 23 51 5 34 1,000 1,360