Determine the optimal z-value

Question

Problem:

1. AA Auto manufactures luxury cars and trucks. The company believes that its most likely customers are high-income women and men. To reach these groups, AA 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 seen by 7 million high-income women and 2 million high-income men. Each football commercial is seen by 2 million high-income women and 12 million high-income men. A 1-minute comedy ad costs $50,000.00 and a 1-minute football ad costs $100,000.00 AA would like the commercials to be seen by at least 28 million high-income women and 24 million high-income men.

The following LP is to determine the minimum cost for ads by AA Auto.

• High-Income Women = HIW
• High-Income Men       = HIM

Min  Z = 50x₁+100x₂

             7x₁+2x₂≥28(HIW)

  S.t.      2x₁+12x₂≥24(HIM)

In the above example, let c1 be the objective function coefficient of . Determine the optimal z-value as a function of c1.