Slack Variables at the Solution Point

At each corner point solution, values for each slack variable are also determined. For example, at the optimal solution (corner M) reached in the preceding section, SA and SB both equal zero, meaning that inputs A and B are used to the fullest extent possible. SC is not equal to zero and must be solved for. To find the solution for SC, QY = 4 is substituted into Constraint Equation 9.9:

The optimal combination of x and Y completely exhausts available quantities of inputs A and B, but 9 units of input C remain unused. Because inputs A and B impose effective constraints on the firm's profits, more of each must be acquired to expand output. Input C is in excess supply, so the firm would certainly not want more capacity of C; it might even attempt to reduce its purchases of C during future periods. If C is a fixed facility, such as a machine tool, the firm might offer some of that excess capacity to other companies.

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