Dorian Auto manufactures luxury cars and trucks. The company believes that its most likely customers are high-income women (HIW) and high income men (HIM). To reach these groups, Dorian Auto has embarked on an ambitious TV advertising campaign and has decided to purchase 1-minute commercial spots on two types of programs: comedy shows and football games. Each comedy commercial is seen by 7 million HIW and 2 million HIM. Each football commercial is seen by 2 million HIW and 12 million HIM. A 1-minute comedy ad costs $50,000, and a 1-minute football ad costs $100,000. Dorian would like the commercials to be seen by at least 28 million HIW and 24 million HIM.
1. Formulate and solve an LP to help Dorian Auto meet its advertising at minimum cost.
2. Find the range of values of the cost of a comedy (currently $50,000) for which the current basis remains optimal
3. Find the range of values of the number of required HIW exposures (currently 28 million) for which the current basis remain optimal. If 40 million HIW exposures were required, what would be the new optimal solution?
4. Suppose an ad on a news program costs $110,000 and reaches 12 million HIW and 7 million HIM. Should Dorian advertise on the news program?