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Set_2_more_simplex - Dr Maddah ENMG 500 Engineering...

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1 Dr. Maddah ENMG 500 Engineering Management I 10/21/07 Computational Procedure of the Simplex Method The optimal solution of a general LP problem is obtained in the following steps: Step 1. Express the problem in tableau form. Step 2. Select a starting basic feasible (BF) solution. This step involves two cases: a) If all the constraints in the original problem are “≤” and RHS > 0, the stack variables give the starting BF solution. b) Otherwise, a technique called the artificial variables technique is used to give a starting BF solution. Step 3. Generate new BF solutions using both the optimality and feasibility conditions until the optimal solution is reached. Optimality conditions For max problems, the entering variable is selected as the nonbasic variable having the most negative coefficient in the objective function row (Z-row). For min problems, select the most positive. Break ties at random. If all Z-row coefficients are nonnegative (for max problems) or nonpositive (for min problems), the optimal solution has been reached. Note the optimal solution. Stop. Feasibility conditions The leaving variable for max and min problems is the basic variable with the smallest ratio of the RHS to the positive constraint coefficient of the entering variable (denominator). If denominator ≤ 0, ignore the corresponding variable. Break ties at random.
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2 Artifi cial variables technique (the “Big” M method) For problems with “ ≥” and “=” constraints, the slack variables cannot provide a starting feasible solution.
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