Suppose that you were a car company’s production planner. The unit wholesale pri

Question

Suppose that you were a car company’s production planner. The unit wholesale price per unit of the company’s branded car is Sedan $16,000, Van $35,000, and SUV $49,000. The variable costs are 4,200QS + QS2 for Sedan production; 10,000QV + QV2 for Van production; and 14,000QU + QU2 for SUV production.

The factory’s monthly production capacity constraint is QS + 1.5QV + 2QU = 60000. With this capacity, the factory has a monthly fixed cost of $50,000,000.

At the coming board meeting, you need to report the maximum profit this factory can make. Use Excel solver to find the optimal quantities of these vehicles the factory should produce per month and the profit.

Explanation / Answer

We have the following profit maxization problem at hand

Max profit Z =  (16,000QS + 35,000QV + 49,000QU) - (50,000,000 + 4,200QS + QS2 + 10,000QV + QV2 + 14,000QU + QU2)

or

Max Z = 11,800QS - QS^2 + 6000QV - QV^2 + 35000QU - QU^2 - 50,000,000

s.t.

QS + 1.5QV + 2QU < or = 60000.

The optimum combination in excel solver for this programming has QS = QV = 0 and QU = 3000. Profit is maximized at 46 million;

Related Questions

Navigate

• Browse (All)
• Browse S
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.