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?

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?

Answer 1

maximize profit = (95 -85) p + (78-72) s + (75-63) e

= 10 p + 6 s + 12 e
subject to constraints:
hours A = 1 p +1 s + 4 e </= 42
hours B = 1 p + 2 s + 3 e </= 40

https://www.easycalculation.com/operations-research/simplex-method-calculator.php

Answer 2

By the way, make 40 premiums.

Answer 3

To solve this problem, we can use linear programming techniques. Let's define the decision variables:

Let P represent the number of Model P tires produced
Let S represent the number of Model S tires produced
Let E represent the number of Model E tires produced

The objective is to maximize the profit, which is given by the difference between the selling price and the cost of production. The total profit can be calculated using the following equations:

Profit for Model P = (95 - 85) * P
Profit for Model S = (78 - 72) * S
Profit for Model E = (75 - 63) * E

The constraints we need to consider are the availability of machine hours:

Machine A constraint: P + S + 4E ≤ 42
Machine B constraint: P + 2S + 3E ≤ 40

Now, let's solve this optimization problem using a mathematical approach called linear programming.

Maximize Z = (95 - 85) * P + (78 - 72) * S + (75 - 63) * E

Subject to:
P + S + 4E ≤ 42
P + 2S + 3E ≤ 40

Since this is a linear programming problem, we can use various optimization software or programming libraries (such as Excel solver, Python SciPy, etc.) to find the solution.

The solution to this optimization problem will give us the values of P, S, and E that maximize the profit and the maximum profit value.