In this chapter, we introduced a mathematical modeling technique called linear programming (LP). It is used in reaching an optimum solution to problems that have a series of constraints binding the objective. We used both the corner point method and the isoprofit/isocost approach for graphically solving problems with only two decision variables.

The graphical solution approaches of this chapter provide a conceptual basis for tackling larger, more complex problems, some of which are addressed in Chapter 8. To solve real-life LP problems with numerous variables and constraints, we need a solution procedure such as the simplex algorithm, the subject of Module 7. The simplex algorithm is the method that QM for Windows and Excel use to tackle LP problems.

In this chapter, we also presented the important concept of sensitivity analysis. Sometimes referred to as postoptimality analysis, sensitivity analysis is used by management to answer a series of what-if questions about LP model parameters. It also tests just how sensitive the optimal solution is to changes in profit or cost coefficients, technological coefficients, and right-hand-side resources. We explored sensitivity analysis graphically (i.e., for problems with only two decision variables) and with computer output, but to see how to conduct sensitivity algebraically through the simplex algorithm, read Module 7 (located at www.pearsonhighered.com/render).