American Auto is evaluating their marketing plan for the sedans, SUVs, and trucks they produce. A TV ad featuring this SUV has been developed. The company estimates that each showing of this commercial will cost $500,000 and increase sales of SUVs by 3%, but reduce sales of trucks by 1%, and have no effect of the sales of sedans. The company also has a print ad campaign developed that it can run in various nationally distributed magazines at a cost of $750,000 per title. It is estimated that each magazine title the ad runs in will increase the sales of sedans, SUVs, and trucks by 2%, 1%, and 4%, respectively. The company desires to increase sales of sedans, SUVs, and trucks by at least 3%, 14%, and 4%, respectively, in the least costly manner.

a. Formulate an LP model for this problem.

b. Sketch the feasible region.

c. What is the optimal solution?