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Linear Prog COP4355_Part_1

Linear Prog COP4355_Part_1 - Chapter 2 Linear Programming...

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8 Chapter 2 Linear Programming: Problem Formulation SOLUTIONS TO END-OF-CHAPTER PROBLEMS: Chapter 2 Linear Programming: Problem Formulation 2.1 Let X 1 = number of newspaper ads X 2 = number of radio ads MAX: 180X 1 + 700X 2 Subject to: 50X 1 + 500X 2 < 2000 (Cost, $) X 1 - 3X 2 > 0 (Ratio:newspaper:radio) (X 1 , X 2 ) > 0 (Nonnegativity) 2.2 Let X 1 = number of regular cheeseburgers X 2 = number of double cheeseburgers MAX: 2.50X 1 + 3.0X 2 Subject to: 4X 1 + 8X 2 < 320 (Hamburger, ozs.) 1X 1 + 2X 2 < 90 (Cheese, ozs.) 1X 1 + 1X 2 < 120 (Buns) (X 1 , X 2 ) > 0 (Nonnegativity) 2.3 Let X 1 = pounds of soybeans X 2 = pounds of wheat X 3 = pounds of oats X 4 = pounds of corn X 5 = pounds of mineral supplement MIN: 0.15X 1 + 0.25X 2 + 0.10X 3 + 0.20X 4 + 0.18X 5 Subj.to: 0.6X 1 - 0.4X 2 - 0.4X 3 + 0.6X 4 - 0.4X 5 > 0 (40% Corn & Soy) - 0.2X 1 + 0.8X 2 - 0.2X 3 - 0.2X 4 - 0.2X 5 < 0 (20% Wheat) - 0.3X 1 - 0.3X 2 + 0.7X 3 - 0.3X 4 - 0.3X 5 > 0 (30% Oats) - 0.1X 1 - 0.1X 2 - 0.1X 3 - 0.1X 4 + 0.9X 5 > 0 (10% Min Sup) X 1 + X 2 + X 3 + X 4 + X 5 = 1000 (Bag weight) (X 1 , X 2 , X 3 , X 4 , X 5 ) > 0 (Nonnegativity) Because the weight of each bag is known, an alternative formulation can be used:
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Solutions Manual and Workbook 9 MIN: 0.15X 1 + 0.25X 2 + 0.10X 3 + 0.20X 4 + 0.18X 5
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