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# chapter 1 - 8. a. Maximize 10x + 5y s.t. 5x + 2y 40 x 0, y...

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8. a. Maximize 10 x + 5 y s.t. 5 x + 2 y 40 x 0, y 0 b. Controllable inputs: x and y Uncontrollable inputs: profit (10,5), labor hours (5,2) and labor-hour availability (40) c. Profit: Labor Hours: 5/unit for x 2/ unit for y \$10/unit for x \$ 5/ unit for y 40 labor-hour capacity Uncontrollable Inputs Production Quantities x and y Controllable Input Projected Profit and check on production time constraint Output Max 10 x + 5 y s.t. 10 x y + 5 40 x y 0 0 Mathematical Model d. x = 0, y = 20 Profit = \$100 (Solution by trial-and-error) e. Deterministic - all uncontrollable inputs are fixed and known. 10. a. Total Units Received = x + y b. Total Cost = 0.20 x +0.25 y c. x + y = 5000 d. x 4000 Kansas City Constraint y 3000 Minneapolis Constraint e. Min 0.20 x + 0.25 y s.t. x + y = 5000 x 4000 y 3000 x , y 0 11. a. at \$20 d = 800 - 10(20) = 600 at \$70 d = 800 - 10(70) = 100

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b. TR = dp = (800 - 10 p ) p = 800 p - 10 p 2 c. at \$30 TR = 800(30) - 10(30) 2 = 15,000 at \$40 TR = 800(40) - 10(40) 2 = 16,000 at \$50 TR = 800(50) - 10(50) 2 = 15,000 Total Revenue is maximized at the \$40 price. d. d = 800 - 10(40) = 400 units TR = \$16,000 12. a. TC = 1000 + 30 x b. P = 40 x - (1000 + 30 x ) = 10 x - 1000 c. Breakeven when P = 0 Thus 10 x - 1000 = 0 10 x = 1000 x = 100 15. a. Profit = 100,000 x
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## This note was uploaded on 04/20/2010 for the course IE ie200 taught by Professor . during the Spring '10 term at 카이스트, 한국과학기술원.

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chapter 1 - 8. a. Maximize 10x + 5y s.t. 5x + 2y 40 x 0, y...

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