Simplex Method for Standard Maximization Problem
Required knowledge: .NET, C#, Delphi, Joomla, PHP
Convert to a system of equations by introducing slack variables to turn the constraints into equations, and rewriting the objective function in standard form. Write down the initial tableau. Select the pivot column: Choose the negative number with the largest magnitude in the bottom row (excluding the rightmost entry). Its column is the pivot column. (If there are two candidates, choose either one.) If all the numbers in the bottom row are zero or positive (excluding the rightmost entry), then you are done: the basic solution maximizes the objective function (see below for the basic solution). Select the pivot in the pivot column: The pivot must always be a positive number. For each positive entry b in the pivot column, compute the ratio a/b, where a is the number in the Answer column in that row. Of these test ratios, choose the smallest one. The corresponding number b is the pivot. Use the pivot to clear the column in the normal manner (taking care to follow the exact prescription for formulating the row operations described in Chapter 2) and then relabel the pivot row with the label from the pivot column. The variable originally labeling the pivot row is the departing or exiting variable and the variable labeling the column is the entering variable. |
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