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HW_Ex_Ch5_Solver

HW_Ex_Ch5_Solver - 5-5 Exercise#5-5 Glass items Profit per...

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5-5 Page 1 Exercise #5-5 Glass items Decanters Trays Profit per item 50 10 Resource constraints Available Usage glass (lbs) 1 1 15 7 labor (hrs) 4 1 25 25 Production: Decanters= 6 Trays= 1 Profit= 310 (a) x1 = # of decanters, x2 = # of trays maximize Z = 50x1 + 10x2 subject to x1 + x2 ≤ 15 (glass, lbs) 4x1 + x2 ≤ 25 (Labor, hours) x1,x2 ≥ 0 and integer (b) x1 = 6, x2 = 1, Z = 310
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5-8 Page 3 Exercise #5-8 Investments: Condominiums Land Annual return ($) 8000 6000 Resource constraints funds ($) 70000 30000 annual expenses ($) 1000 2000 Investments: Condominiums= 5 units Land= 4.5 acres Profit= 67,000 a) x1 = condominium, x2 = land maximize Z = $8000x1 + 6000x2 subject to 70000x1 + 30000x2 ≤ 500000 (investment $) 1000x1 + 2000x2 ≤ 14000 (maintenance $) x1 ≥ 0 and integer x2 ≥ 0 (b) x1 = 5, x2 = 4.5, Z = 67,000
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5-8 Page 4 Available Usage Left over 500000 485000 15000 14000 14000 0
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5-9 Page 5 Exercise #5-9 Machines Lathe Press Grinder Profit per machine 1000 700 800 Resource constraints Available Usage purchase price ($) 5000 6000 4000 10000 9000 Purchases Lathe= 1 Press= 0 Grinder= 1 Profit= 1800 x1=lathe, x2= press, x3 = grinder maximize Z = 1,000x1 + 700x2 + 800x3 subject to x1, x2, x3 = 0 or 1 x1 = 1, x2 = 0, x3 = 1, Z = 1,800 $5,000x1 + 6,000x2 + 4,000x3 10,000 (cost, $)
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