Question
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 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?
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 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?
Answers
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 constraints, and evaluate p at the vertices of the region shown.
p = (95-85)x + (78-72)y + (75-63)z = 10x+6y+8z
Now write constraints, and evaluate p at the vertices of the region shown.