Linear Programming

The K9 Kondo Company manufactures climate-controlled doghouses. The company believes that its high-volume customers are high-income male and female dog owners who want to pamper their pets. To reach these groups, the marketing manager at K9 Kondo is considering placing one-minute commercials on the following national TV shows: “New York Dog Show” and “Man's Best Friend.” A one-minute commercial on “New York Dog Show” costs $200,000, and a one-minute commercial on “Man's Best Friend” costs $50,000. The marketing manager would like the commercials to be seen by at least 60 million high-income women and at least 36 million high-income men. Marketing studies show the following:

• Each one-minute commercial on “New York Dog Show” is seen by six million high-income women and two million high-income men.
• Each one-minute commercial on “Man's Best Friend” is seen by three million high-income women and three million high-income men.

How many one-minute commercials should they air on each show to minimize the cost? What is that minimum cost?