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Unformatted text preview: Algebraic Solution of LPPs  Simplex Method To solve an LPP algebraically, we first put it in the standard form . This means all decision variables are nonnegative and all constraints (other than the nonnegativity restrictions) are equations with nonnegative RHS. Converting inequalities into equations 2 1 3 2 x x z + = Subject to , 6 2 3 6 3 2 1 2 1 2 1 ≥ ≤ + ≤ + x x x x x x Maximize Consider the LPP We make the ≤ inequalities into equations by adding to each inequality a “slack” variable (which is nonnegative). Thus the given LPP can be written in the equivalent form 2 1 3 2 x x z + = Subject to , , , 6 2 3 6 3 2 1 2 1 2 2 1 1 2 1 ≥ = + + = + + s s x x s x x s x x are slack variables. 2 1 , s s Maximize Thus we seem to have complicated the problem by introducing two more variables; but then we shall see that this is easier to solve. This is one of the “beauties” in mathematical problem solving. The ≥ inequalities are made into equations by subtracting from each such inequality a “surplus” (nonnegative) variable. Thus the LPP 2 1 3 2 x x z + = Subject to , 2 2 3 6 3 2 1 2 1 2 1 ≥ ≥ + ≤ + x x x x x x Maximize is equivalent to the LPP 2 1 3 2 x x z + = Subject to , , , 2 2 3 6 3 2 1 2 1 2 2 1 1 2 1 ≥ =+ = + + s s x x s x x s x x is a slack variable; is a surplus variable....
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 Spring '11
 Rashid
 Optimization, X1

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