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A3.1. AN EXAMPLE

We use a variation of Example 2.1 to illustrate how the simplex method works. For this purpose, we drop the wood constraint and address the following optimization problem.

The simplex method works not with inequalities but rather with equalities, so our first step is to recast the constraints of the model as equations. To do so, we introduce three additional variables that account for unused amounts of the three resources. In other words, these variables represent the difference between the right-hand side (RHS) and left-hand side (LHS) of the constraints, as they are posed above. The constraints may be written as follows.

The variables u, v, and w are called slack variables: they measure the amount of slack, or unused resource, in each constraint. These three variables, like the three original decision variables C, D, and T, are all considered to be nonnegative. (We assume throughout that all variables are nonnegative.)