4. A sales manager seeks to optimize her advertising budget. Her goal is to obtain 160 million "Exposures" (readers and/or viewers exposed to an ad for the company). Seeking a younger, affluent audience, the firm would like at least 50 million of the exposures to be persons between the ages of 25 and 45. In addition the firm would like at least half of all exposures to be persons with an income over $35,000 per year. Each magazine ad (M) costs $175,000 and reaches an audience of 10 million persons. TV ads (T) each cost $300,000 to produce and air, and reach an audience of 20 million persons. About 75% of magazine readers are persons in the target income bracket, and about 60% of the readers are persons in the target age bracket. About 25% of TV viewers are persons in the target income bracket and about 12.5% of the viewers are in the target age bracket.
a. Formulate the linear programming problem.
b. Graph the feasible space.
c. Compute the solution.