Engineering Optimization: Theory and Practice, Fourth Edition

126 Linear Programming I: Simplex Method

Figure 3.4 Contours of objective function.

In some cases, the optimum solution may not be unique. For example, if the

profit rates for the machine parts I and II are $40 and $100 instead of $50 and $100,

respectively, the contours of the profit function will be parallel to sideCG of the

feasible region as shown in Fig. 3.5. In this case, lineP′′Q′′, which coincides with the

boundary lineCG, will correspond to the maximum (feasible) profit. Thus there is no

unique optimal solution to the problem and any point betweenCandGon lineP′′Q′′

Figure 3.5 Infinite solutions.