Question

Technostrain Corporation manufactures two products: X and Y. The company has 4,000 hours of machine time available and can sell no more than 800 units of product X. Other pertinent data follow.

	Product X				Product Y
Selling price	$	8.00			$	19.00
Variable cost		3.00				5.00
Fixed cost		3.50				6.25
Machine time per unit	2 hours				3 hours

Which of the following is Technostrain’s objective function?

Multiple Choice

• Maximize Z = 8X + 19Y.

• Maximize Z = 1.50X + 7.75Y.

• Maximize Z = 5X + 14Y.

• Minimize Z = 6.50X + 11.25Y.

• Maximize Z = 2X + 3Y.

Answer 1

Answer)

In the given problem, the objective function will be formed in such a way so as to maximize profits.

Formula:

Profit = Sales – Variable Cost – Fixed Cost

Let the number of units of Product X to be sold be ”X” and of product Y be “Y”.

Profit for Product X = Sales of Product X – Variable cost of Product X – Fixed Cost for Product X

                                    = (Selling price per unit X number of units sold) – (Variable cost per unit X number of units sold) – (Fixed cost per unit X number of units sold)

                                                  = $ 8X - $ 3X - $ 3.50X

                                                   = $ 1.50X

Profit for Product Y = Sales of Product Y – Variable cost of Product Y – Fixed Cost for Product Y

                                    = (Selling price per unit X number of units sold) – (Variable cost per unit X number of units sold) – (Fixed cost per unit X number of units sold)

                                                  = $ 19Y - $ 5Y - $ 6.25Y

                                                   = $ 7.75Y

Total Profit = Profit from Product X + Profit from Product Y

Total Profit = 1.50X + $ 7.75Y   

Since total profit is to be maximized, the objective function will be:

Maximize Z = $ 1.50X + $ 7.75Y