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Linear Prog COP4355_Part_2

# Linear Prog COP4355_Part_2 - 12X 1 36X 2 Subject to 2X 1 4X...

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12 Chapter 2 Linear Programming: Problem Formulation 2.13 Let X 1 = ozs. of beef X 2 = ozs. of pork X 3 = ozs. of chicken X 4 = ozs. of filler MIN: 0.10625X 1 + 0.0625X 2 + 0.059375X 3 + 0.01875X 4 Subject to: X 1 + X 2 + X 3 + X 4 = 16 (Tot.Wt.=16 ozs) X 2 < 1.6 (Amt.pork, 10%) X 3 4 (Amt.chick. 30%) X 1 > 4.8 (Amt.beef, 30%) 5X 1 + 3X 2 + 4X 3 + 1X 4 > 10 (Min. mgs.Pro.) 3X 1 + 5X 2 + 2X 3 + 3X 4 < 4 (Max. mgs.Fat) 3X 1 +10X 2 + 4X 3 + 3X 4 < 8 (Max. mgs.Water) (X 1 , X 2 , X 3 , X 4 ) > 0 (Nonnegativity) 2.14 Let X 1 = amount invested in gold X 2 = amount invested in bonds X 3 = amount invested in savings accounts X 4 = amount invested in common stock MAXIMIZE: 0.06X 1 + 0.09X 2 + 0.04X 3 + 0.15X 4 Subject to: X 1 + X 2 + X 3 + X 4 = 10000 (Tot. Invest., \$) X 2 + X 3 < 2000 (Sav. & bonds: 20%) X 1 > 500 (Gold, 5%) X 4 < 6000 (C. Stk. 60%) (X 1 , X 2 , X 3 , X 4 ) > 0 (Nonnegativity) 2.15 Let X 1 = units of product 1 X 2 = units of product 2 MAXIMIZE:

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Unformatted text preview: 12X 1 + 36X 2 Subject to: 2X 1 + 4X 2 < 500 (Work Center 1 Capacity) 2X 1 + 6X 2 < 800 (Work Center 2 Capacity) 4X 1 + 6X 2 < 1000 (Work Center 3 Capacity) (X 1 , X 2 ) > 0 (Nonnegativity) 2.16 Let X 1 = acres of lettuce X 2 = acres of potatoes X 3 = acres of tomatoes X 4 = acres of beans MAXIMIZE: 90X 1 + 85X 2 + 100X 3 + 50X 4 Solutions Manual and Workbook 13 Subject to: 10000X 1 < 40000 (Dem. Lettuce) 40000X 2 < 100000 (Dem. potatoes) 2000X 3 < 50000 (Dem. tomatoes) 1000X 4 < 4000 (Dem. beans) X 1 + X 2 + X 3 + X 4 = 10 (Acres used = 10) (X 1 , X 2 , X 3 , X 4 ) > 0 (Nonnegativity) 14 Chapter 3 Linear Programming: Graphical Analysis Chapter 3 Linear Programming: Graphical Analysis Solutions Manual and Workbook 15...
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Linear Prog COP4355_Part_2 - 12X 1 36X 2 Subject to 2X 1 4X...

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