A brand manager for ColPal Products must determine how much time to allocate between radio and television advertising during the next month. Market research has provided estimates of the audience exposure for each minute of advertising in each medium, which it would like to maximize. Costs per minute of advertising are also known, and the manager has a limited budget of $25,000. The manager has decided that because television ads have been found to be much more effective than radio ads, at least 70% of the time should be allocated to television. Suppose that we have the following data:

Components Required/unit
Radio TV
Exposure/Minute 350 800
Cost/Minute 400 2000
Minimum allocation - 0.7

a. identify the decision variables
b. Mathematically formulate a linear optimization model
c. Solve the model using Excel solver
d. Get sensitivity report

e. Answer the following questions:

1. Suppose that the exposure for TV advertising was incorrectly estimated and should have been 875. How would the optimal solution have been affected?
2. Radio listening has gone down, and new marketing studies have found that the exposure has dropped to 150. How will this affect the optimal solution?
3. The marketing manager has increased the budget by $2,000. How will this affect the solution and total exposure?