a company makes three types of cars, midsize and SUV. A compact car requires 20

Question

a company makes three types of cars, midsize and SUV. A compact car requires 20 hours of labor and $10,000 in supplies. A midsize car requires 30 hours of labor and $15,000 in supplies. An SUV requires 35 hours of labor and $25,000 in supplies. Each week the company has 4000 labor hours available and 2 million dollars to spend on supplies. Each compact car brings a profit of $5,000, each midsize car brings a profit of $6,000 and each SUV brings a profit of $10,000. The weekly total demand for all of the cars is at most 75 cars. The goal is to maximize weekly profits. I need to determine what is the objective function, labor constraint and demand constraint.

Explanation / Answer

Let x, y and z represents the number of cars to be manufactured in order to achieve maximum profit.

Objective function,
Max Z = 5000x + 6000y + 10000z

subject to,

Labor constraint
20x + 30y + 35z <= 4000

Demand Constraint
x + y + z <= 75

Supplies constraint
10000x + 15000y + 25000z <= 2000000

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