Mat 122 Linear Programming Project

Mat 122 Linear Programming Project - 6x + 9y 300 5x + 4y...

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MAT 122 Finite College Math MAT 122 Linear Programming Project Objective: Use Graphing and the Simplex Method to solve a Linear Programming problem Project A: 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 $3 on each unit of Product A and a profit of $4 on each unit of Product B. To manufacture a unit of Product A requires 6 minutes on Machine I and 5 minutes on Machine II. To manufacture a unit of Product B requires 9 minutes on Machine I and 4 minutes on Machine II. There are 300 minutes of machine time available on Machine I and 180 minutes of machine time available on Machine II in each work shift. How many unites of each product should be produced in each shift to maximize the company’s profit? Products A B Total Machine I 6 min. 9 min. ≤ 300 min./shift Machine II 5 min. 4 min. ≤ 180 min./shift Profit $3 $4 P Maximize – P = 3x + 4x Subject to: 6x + 9y ≤ 300 5x + 4y ≤ 180 x ≥ 0 y ≥ 0 solve for (y)
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Unformatted text preview: 6x + 9y 300 5x + 4y 180 9y 300 6x 4y 180 5x y 33.3 2/3x y 45 5/4x X Y 33.3 50 X Y 45 36 55 50 45 40 35 30 25 20 15 10 5 5 10 15 20 25 30 35 40 45 50 CORNERS: (0 , 0) P = 3 (0) + 4 (0) = 0 (36 , 0) P = 3 (36) + 4 (0) = 108 (20 , 20) P = 3 (20) + 4 (20) = 140 (0 , 33.3) P = 3 (0) + 4 (33.3) = 133.2 SIMPLEX METHOD: Maximize P = 3x + 4y -3x 4y + P = 0 Subject to: 6x + 9y 300 6x + 9y + s = 300 5x + 4y 180 5x + 4y + s = 180 Initial Simplex Tableau x y s s P C 6 9 1 30 5 4 1 18-3-4 1 1 st Pivot x y s s P c .7 1 .1 33.3 2. 3-. 4 1 46.7-.3 .4 1 400/ 3 Final Simplex Matrix x y s s P C 1 .2-. 3 20 1-. 2 .4 20 .4 .1 1 14 x = 20 y = 20 P 140 s = 0 s = 0 This data shows us that the company needs to manufacture 20 units of Product A and 20 units of Product B each shift to make the maximum profit of $140....
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This note was uploaded on 11/18/2011 for the course MATH 122 taught by Professor Smith during the Spring '10 term at Lander.

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Mat 122 Linear Programming Project - 6x + 9y 300 5x + 4y...

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