We want to select an advertising strategy to reach two types of customers: homemakers in families with over $50,000 annual income and homemakers in families with under $50,000 income. We feel that people in the first group will purchase twice as much of our product as people in the second group, and our goal is to maximize purchases.
We may advertise either on TV or in a magazine; one unit of TV advertising costs $20,000 and reaches approximately 2,000 people in the first group and 8,000 people in the second group. One unit of advertising in the magazine costs $12,000 and reaches 6,000 people in the first group and 3,000 people in the second group. We require that at least 6 units on TV advertising be used and that no more than 12 units of magazine advertising be used, for policy reasons. The advertising budget is $180,000.
Formulate this problem as a linear programming problem. Clearly define your decision variables and identify what each constraint refers to.