To use the Simplex method, a given linear programming model needs to be in standard form, where slack variables can then be introduced. The method produces an optimal solution to satisfy the given constraints and produce a maximum zeta value. The Simplex method is an approach for determining the optimal value of a linear program by hand. The maximum optimal value is 2100 and found at (0,0, 350) of the objective function. Due to 350 being the smallest non-negative ratio, the pivot value will be in the second row which is highlighted in green and intersection for pivot row and column will be pivot element which has a value of 1 which is highlighted in Red color. Solving for the ratio gives us a value of (900/1 = 900) for the first constraint, a value of (350/1 = 350) for the second constraint, and value of third constraint (400/1 = 400). The intersection of the row with the smallest non-negative indicator and the smallest negative value in the bottom row will become the pivot variable.ĭivide the pivot column with constant in corresponding row and identify the values. To find the indicator, divide the beta values of the linear constraints by their corresponding values from the column containing the possible pivot variable.
One of the values lying in the column of this value will be the pivot variable. Assuming that the solution is not optimal, pick the smallest negative value in the bottom row. The pivot variable can be identified by looking at the bottom row of the tableau and the indicator. The pivot variable is used in row operations to identify which variable will become the unit value and is a key factor in the conversion of the unit value. This will designate the z column to contain the pivot variable which is highlighted by yellow. In the above table, -6 is the smallest negative in the last row.
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