HW2_Solutions

# HW2_Solutions - OSCM 230 Homework 02 HOMEWORK #2 LINEAR...

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OSCM 230 Homework 02 H O M E W O R K # 2 L I N E A R P R O G R A M M I N G ( L P ) F O R M U L A T I O N 3-2. Let C = number of canvas backpacks produced. P, N, L defined similarly. Objective: Maximize profit = (Canvas revenue – Canvas cost)*C + (Plastic revenue – Plastic cost)*P + (Nylon revenue – Nylon cost)*N + (Leather revenue – Leather cost)*L = Maximize \$14.88C + \$18.80P + \$12.80N + \$27.83L Subject to: 2.25C 200 Canvas available 2.40P 350 Plastic available 2.10N 700 Nylon available 2.60L 550 Leather available 1.5C + 1.5P 90 1.7N 42. 5 Nylon labor 1.9 L 80 Leather labor C, P, N, L 40 Max production C, P, N, L 15 Min production Solution: See File P3-2.XLS. Produce 20 Canvas, 40 Plastic, 25 Nylon, and 40 Leather backpacks. Profit = \$2,483.58. 3-5. Let C = number of cheese pizzas to order. P and V defined similarly. Objective: Maximize profit = \$1.45C + \$1.75P + \$1.98V Subject to: C + + V 350 Total pizzas C 120 Max cheese P 150 Max pepperoni V 100 Max vegetarian C 0.2(C+P+V) Min cheese P 0.5(C+P+V) Min pepperoni C, P, V 0 Non-negativity Solution: See file P3-5.XLS. Order 60 cheese, 150 pepperoni, and 90 vegetarian pizzas. Profit = \$527.70. Page 1 of 6

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OSCM 230 Homework 02 3-6. Let C = number of Chaunceys mixed. S, B, and R defined similarly. Objective: Maximize total drinks = C + S + B + R Subject to 1C + 4B 64 (bourbon limit, oz) 1C + 1S 38 (brandy limit oz) 1C + 3R 70 (vodka limit oz) 1S + 1R 30 (dry vermouth limit oz) 1C + 2S 40 (sweet vermouth limit oz) C, S, B, R 0 Solution: See file P3-6.XLS. Mix 16 Chaunceys, 12 Sweet Italians, 12 Bourbon on the rocks, and 18 Russian martinis. Total = 58 drinks. 3-18. Let X i = number of workers starting work at period i (with i = 1, 2, 3, 4, 5, or 6) Objective: Minimize staff size = X 1 + X 2 + X 3 + X 4 + X 5 + X 6 Subject to: X 1 + X 2 12 X 2 + X 3 16 X 3 + X 4 9 X 4 + X 5 11 X 5 + X 6 4 X 1 + X 6 3 All variables 0 Solution: See file P3-18.XLS. Hire 30 workers. 12 start at 7am, 4 start at 11am, 10 start at 3pm, 1 starts at 7pm, and 3 start at
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## This note was uploaded on 09/21/2009 for the course B 362 taught by Professor Trus during the Spring '09 term at Washington University in St. Louis.

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HW2_Solutions - OSCM 230 Homework 02 HOMEWORK #2 LINEAR...

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