Reference no: EM13879698

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 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. Your boss tells you that you can't spend more than $200,000 on this project. Furthermore, the radio and TV stations tell you they 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. The boss tells you that he doesn't want more than 15 TV commer- cials because he gets sick of watching the same thing over and over again. The objective is to find the combination of TV (x) and radio (y) commercials that maxi- mize the sale of milk.

a. Set up this problem as an LP model.

b. Write this problem in standard form (using slack variables) and in general form without slack variables.

c. Graph the feasible region for this problem.

d. Find the optimal solution for this problem.