Quantitative Analysis for Management, 13/e

Slack and Surplus

The term slack is associated with ≤ constraints.

In addition to knowing the optimal solution to a linear program, it is helpful to know whether all of the available resources are being used. The term slack is used for the amount of a resource that is not used. For a less-than-or-equal-to constraint,

$$\text{Slack}=\left(\text{Amount of resource available}\right)-\left(\text{Amount of resource used}\right)$$

In the Flair Furniture example, there were 240 hours of carpentry time available. If the company decided to produce 20 tables and 25 chairs instead of the optimal solution, the amount of carpentry time used $\left(4\text{T}+3\text{C}\right)$ would be $4\left(20\right)+3\left(25\right)=155.$ So

$$\text{Slack time in carpentry}=240-155=85$$

For the optimal solution $\left(30\text{, }40\right)$ to the Flair Furniture problem, the slack is 0, since ...