Cost per ad
Total audience per ad
Audience per ad with income >$50,000
Unmarried audience per ad
10,000R + 20,000TV - SA = 100,000 10,000R + 10,0007V - Sj = 80,000 8,000R + 4,0007V - SS = 40,000
SA, SI, and SS are slack variables indicating the extent to which minimums on total audience exposure, exposure to individuals with incomes of at least $50,000, and exposure to single individuals, respectively, have been exceeded. Note that each slack variable is subtracted from the relevant constraint equation because greater-than-or-equal-to inequalities are involved. Excess capacity or nonzero slack variables for any of the constraints mean that audience exposure minimums have been exceeded.
The solution to this linear programming problem is easily obtained using a combination of graphic and analytical methods. Figure 9.10 illustrates this solution. The feasible space problem
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