You have just been hired as an advertising manager for a generic advertising program for dairy farmers, Dairy Management, Inc. (DMI). DMI wants to conduct generic advertising to increase the demand for milk. DMI has decided to consider both TV and radio, and wants you to do an analysis of how many TV and radio commercials to pur- chase for the month. You expect that one TV commercial will increase sales by 25,000 gallons and one radio commercial will increase sales by 7,000 gallons. It costs $10,000 per TV commercial and $5,000 per radio commercial. You have a budget of $200,000 for this project.
Furthermore, the radio and TV stations have a combined maximum of 90 minutes for your commercials for the month. Each TV commercial takes 1 minute, and each radio commercial takes 2 minutes to air. Marketing research indicates that milk consumers do not want more than 15 TV commercials because they find watching the same commercial multiple times irritating. The objective is to find the combination of TV (x) and radio (y) commercials that maximize the sale of milk. Solve this problem using the simplex method.