If there are x P tires, y S tires, and z E tires, then the profit function is
p = (95-85)x + (78-72)y + (75-63)z = 10x+6y+8z
Now write the constraints, and evaluate p at the vertices of the region graphed.
Ace Rubber company manufacture three types of tires: Model P, the premium, Model S, the second line, and Model E, the economy. Model P sells for Birr 95 per tire and costs Birr 85 per tire to make, Model S sells for Birr 78 per tire and costs Birr 72 per tire to make, while Model E sells for Birr 75 per tire and costs Birr 63 per tire to make. To make one Model P tire, it requires one hour on machine A and one hour on machine B. To make one Model S tire, it takes one hour on machine A and two hours on machine B; to make one model E tire requires four hours on A and three hours on B. Production scheduling indicates that during the coming week machine A will be available for at most 42 hours and machine B for at most 40 hours. How many of each tire should the company make in the coming week in order to maximize its profit? What is the maximum profit?
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