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Set_1_a_LPintro_graphical - Dr Maddah ENMG 500 Engineering...

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1 Dr. Maddah ENMG 500 Engineering Management I 10/04/06 Introduction ¾ A linear program (LP) is a model of an optimization problem with a linear objective function and linear constraints. ¾ A LP objective is to determine the values of decision variables that maximize or minimize the objective function. ¾ A LP involving maximization with n decision variables and m constraints is represented as follows 1 1 2 2 11 1 12 2 1 1 21 1 22 2 2 2 1 1 2 2 max Z subject to n n n n n n m m mn n n c x c x c x a x a x a x b a x a x a x b a x a x a x b = + + + + + + + + + + + + = # # # 1 2 0, 0, , 0 n x x x ¾ Note that constraints can be of any type “ ”, “ ”, or “=”. ¾ The last set of constraints, x 1 0, …., x n 0, are called nonnegativity constraints. Example ¾ BM Company produces two products, P 1 and P 2 that are sold at $3 and $4 profit margin respectively and require two raw materials, M 1 and M 2 . A unit of P 1 requires 3 units of M 1 and 2 units of M 2 . A unit of P 2 requires 1 unit of M 1 and
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