Appendix: linear programming The LP discussion in this appendix extends the notion, maximise CM per unit of scarce resource, advanced in the chapter in more complex settings with multiple constraints. The objective is to maximise the contribution margin (rather than the profit) per unit of the constraints. Fixed costs are irrelevant, since they are assumed to remain the same regardless of the product mix. Such analysis is most appropriate in the short run where many costs are indeed fixed with respect to the number of units of output. The graphic approach illustrated in Exhibit 10.14 is feasible with two products, three products would require a three-dimensional graph, etc. Stress that we use the graphic approach to help students develop an intuitive understanding of the basic concepts. In practice, the graphic solution is almost never used, since most LP problems involve numerous products and constraints. Companies use calculator software packages programmed to solve large LP problems. The discussion of the intuition underlying LP helps students understand why LP works. The basic point is that LP systematically analyses the exchange of a given CM per unit of scarce resource for some other contribution margin of scarce resource in order to find the optimal product mix (highest contribution margin or lowest cost. This section shows that large changes in contribution margin per unit of product may not affect the optimal product mix if there are no other nearby corner points.
