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Linear_Programming_Formulation_Examples

# Linear_Programming_Formulation_Examples - Example 1...

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Example 1: Product-Mix Problem A company manufactures three models of a electrical product. The following table summarizes the requirements for the two major resources in the production process. Model A B C Labor (hours/unit) 7 3 6 Material (lb/unit) 4 4 5 Profit Margin \$4 \$2 \$3 The supply of raw material is restricted to 200 pounds per day while the daily available labor is 150 hours. Formulate a linear programming model to maximize total profit.

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Definition of decision variables Define x 1 as the daily production of model A. Define x 2 as the daily production of model B. Define x 3 as the daily production of model C. 3 2 1 3 2 4 x x x + + Definition of objective function Maximize Profit, Z = 3 2 1 6 3 7 x x x + + Identifying the constraints Subject to: 150 3 2 1 5 4 4 x x x + + 200 3 2 1 , , x x x 0
Example 2: Blending/Mixing Problem The Munchies Cereal Company makes a cereal from several ingredients. Two of the ingredients, oats and rice, provide vitamins A and B. The company wants to know how many ounces of oats and rice it should include in each box of cereal to meet the minimum requirements of 48 mg of vitamin A and 12 mg of vitamin B while minimizing cost. An ounce of oats contributes 8 mg of vitamin A and 1 mg of vitamin B, whereas an ounce of rice contributes 6 mg of vitamin A and 2 mg of vitamin b. An ounce of oats costs \$0.05, and an ounce of rice costs \$0.03. Formulate a linear programming model for this problem.

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Minimize Cost, W = 2 1 03 . 0 05 . 0 x x + Subject to: 2 1 6 8 x x + 48 2 1 2 x x + 12 0 , 2 1 x x Define x 1 as the amount of oats in ounces to be used/box. Define x 2 as the amount of rice in ounces to be used/box.
A coffee manufacturer blends four component coffee beans into three final blends of coffee. The four component beans cost the manufacturer \$0.65, \$0.80, \$0.90 , and \$0.75 per pound, respectively. The weekly availability of the four components are 80000, 40000, 30000, and 50000 pounds, respectively. The manufacturer sells the three blends at wholesale prices of \$1.25, \$1.40, and \$1.80 per pound, respectively. Weekly output should include at least 50000 pounds of final blend 3 . The following are blending restrictions which must be followed by the brewmaster.

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Linear_Programming_Formulation_Examples - Example 1...

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