## Primal Problem

The objective is to minimize the cost of the advertising campaign. Because total cost is merely the sum of the amounts spent on radio and television advertisements, the objective function is

where R and TV represent the number of radio and television ads, respectively, that are employed in the advertising campaign.

This linear programming problem has three constraint equations, including the minimum audience exposure requirement, the audience income requirement, and the marital status requirement. The minimum audience exposure requirement states that the number of persons exposed to radio ads plus the number exposed to television ads must be equal to or greater than 100,000 persons. Algebraically, 10,000 times the number of radio ads plus 20,000 times the number of television advertisements must be equal to or greater than 100,000:

The two remaining constraints can be constructed in a similar fashion from the data in Table 9.4. The audience income constraint is written

and the marital status constraint is given by

Combining the cost-minimization objective function with these three constraint conditions written in equality form using slack variables gives the complete linear programming problem: