Alternate Optimal Solutions

Sometimes when an optimization model is developed, the model produces many alternative optimal solutions, which means that for the same value of the objective function, the model produces multiple values โ€‹โ€‹of the non-basic or decision variables.

The alternative optimal solution is essentially due to the fact that part of the polyhedron is parallel to the objective function. In such cases all points along the segment segment that are parallel to the obj function will be affine transforms and will have the same value as the obj function.

The implications in a practical situation would be when one is trying to solve the problem of calculating the maximum profit given the effort to produce 10 different products and the total labor constraint available in the plant. Suppose the problem has 10 decision variables and two constraints. Due to the degradation described above it can find the optimal solution with a maximum profit of USD 10000 for multiple combinations of product…

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