A firm makes two products, Y and Z. Each unit of Y costs $10 and sells for $40. Each unit of Z costs $5 and sells for $25. If the firm's goal were to maximize profit, the appropriate objective function would be
A) maximize $40Y = $25Z
B) maximize $40Y + $25Z
C) maximize $30Y + $20Z
D) maximize 0.25Y + 0.20Z
E) none of the above

Question

Quizplus · Accepted Answer

The objective function should represent the total profit of the firm. Since Y and Z have different costs and selling prices, we need to calculate the contribution margin for each product. The contribution margin is the difference between the selling price and the variable cost (the cost that changes with the production level).

For product Y, the contribution margin is $40 - $10 = $30 per unit.
For product Z, the contribution margin is $25 - $5 = $20 per unit.

To maximize profit, the firm should produce more units of the product with the higher contribution margin. The coefficients of the objective function should reflect this fact. Since the contribution margin of Y is $30 and the contribution margin of Z is $20, we can write the objective function as:

Maximize $30Y + $20Z

Therefore, the best choice is C.

A Firm Makes Two Products, Y and Z