Question

-12 Points) DETAILS ASK YOUR TEACHER A company manufactures x units of Product A and y units of Product B, on two machines, I and II. It has been determined that the company will realize a profit of $3/unit of Product A and a profit of $5/unit of Product B. To manufacture a unit of Product A requires 6 min on Machine I and 5 min on Machine II. To manufacture a unit of Product B requires 9 min on Machine 1 and 4 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? (x, y) =( What is the optimal profit? (Round your answer to the nearest whole number.) $ Submit Answer

Answer 1

X?,0 5x+4you en 6x+gy < 300 product A= x Unit Product B = Y unit max profit 3x + sy for machine I (shr=300 min) 6x + gy € 300 for machine I- 52 + 4y = 180 C3h = 480 min) we have system - Zmax = 3x + 5y subject to - 68 +gy & 300 Setay stao 97,0 45 100 3 (20,20) feasible Region y20 36

Feasiable Region corner point- (0,0) (20,20), (0, 100 3 ) (360) to Now find profit corresponding points Point L. 32 3x tsy (0:0) L= 30) + SCO) (0.100) = 3(0) + 5 (100) = $166.67 B: 3(20) + 5(20) = $ 160 (20,20) 2 - 386) + sco) = $ 108 66,0) maximum profit 2$167 A pe = 33.333 3 17 = 33 (x,y) (0,33) optimal profita $ 167

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