Lecture3

2 3 4 5 x1x i maximize z 30x 30x2 10x 15x l l 1 2 l l

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Unformatted text preview: , Maximize z = 30x, +30x2 +10x, +15x, l l 1 2 l l l 2 3 3 2 4 1 2 2 s. t. 500 380 21, + 3.5 +4x, + 21, 5 500 3x, +2x, + I, + 2x, I 380 5, _.r> .I) .x1 2 0 Cost per hour of machine (1, 2) is ($10, $5) Sales price per unit is $65, $70, $55, and 646 Formulate an LP to optimize total Net Protlt Problem 2-28 Standard Form of LP (SOlUtiOtl) A Linear Program is in standard form if: All Constraints have Non-Negative RHS All Constraints are Equations All problem variables are restricted (must be Non-Negative The RHS of the Objective Function I S set equal to zero Profit = Revenue - Expense l l Product 1: 30=65-[(Z)(lO)-(3)(j)] l Product 2: 30 = 70-[(3X IO) -(Z)(j)] Product 3 lt~=jj-((-1X10)-(IXj)] l Product-I Ij=-lj-((Z)(lO)-(2)(j)] EM-602 I QM-710 (NJ) Lecture 3 Page 3-2 Basic Feasible Solution Definitions Given an LP problem with m constraint equatlons and n variables, we define Basic Variable: A Variable whose current value is (In most cases) Non-Zero Non-Basic Variable: A Variable wtth its current value = 0 Basic Feasible Solutlon: The Initial solution set to an LP problem. According to theorem, (n-m) of the problem variables are NonBasic, leaving m Basic variables Identify In the paint company problem which variables are basic and their lnltlal values For each of the m constraint eqUitiOnS, let the slack variable assume the value of the RHS The remaining (n-m) variables in the problem are therefore set equal to zero (Non-Basic) l l l l l Simplex Method Std Form - Paint Co. Simplex Is algebraic equivalent to graphical method Grap...
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This document was uploaded on 03/31/2014 for the course MS 602 at NJIT.

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