GMW Auto manufactures luxury cars and trucks. The company believes that its most likely customers are high-income women and men. To reach these groups, GMW Auto has embarked on an ambitious TV advertising campaign and has decided to purchase commercial spots on two types of programs: Drama show and Super Bowl game. A drama show commercial's length is 1.4-minutes and each drama show commercial is seen by 12 million high-income women and 8 million high-income men. A Super Bowl commercial's length is 0.5-minute and each Super Bowl commercial is seen by 11 million high-income women and 16 million high-income men. GMW Auto has 4.7-minutes of commercial spots available. A 1.4-minutes drama show ad costs $246,000, and a 0.5-minute Super Bowl ad costs $457,000. GMW would like the commercials to be seen by at least 47 million high-income women and 35 million high-income men.
Formulate a linear programming model to determine how GMW Auto can meet its advertising requirements at minimum cost. (Write the complete model for the problem. Make sure to give clear definitions of your decision variables).