Applying linear programming and solving the given equation

Question

A company manufactures two products, A and B, on two machines, I and II. It has been determined that the company will realize a profit of $5/unit of product A and $8/unit of product B. To manufacture a unit of product A requires 11 min on machine I and 7 min on machine II. To manufacture a unit of product B requires 19 min on machine I and 11 min on machine II. There are 5 hr of machine time available on machine I and 3 hr of machine time available on machine II in each work shift. How many units of each product should be produced in each shift to maximize the company's profit?

Model A= _____ Units

Model B= _____ Units

What is the optimal profit?

Answer 1

Objective f(A,B)= 5A+8B

11A + 19B = 5

7A + 11B = 3

77A + 133B = 35

77A + 121B = 33

12B = 2 --> B = 2/12 = 1/6

substitutes:

11A + 19(1/6) = 5

11A + 19/6 = 5

11A= 5 - 19/6 = (30-19)/6 = 11/6 --> A = 1/6

checks:

7A + 11(1/6) = 3

7A = 3 - 11/6 = 7/6

A = 1/6

A=1/6 and B=1/6

5(1/6) + 8(1/6) = 5/6 + 8/6 = 13/6

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