Question: Figure shows the Solver sensitivity report for the ColPal Products scenario in Problem. Using only the information in the sensitivity report, answer the following questions.
a. Suppose that the exposure for TV advertising was incorrectly estimated and should have been 875. How would the optimal solution have been affected?
b. 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?
c. The marketing manager has increased the budget by $2,000. How will this affect the solution and total exposure?
d. The shadow price for the mix constraint (that at least 70% of the time should be allocated to TV) is -250. The marketing manager was told that this means that if the percentage of TV advertising is increased to 71%, exposure will fall by 250. Explain why this statement is incorrect.
Problem: 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:
Type of ad Exposure/Minute Cost/Minute
Radio 350 $400
Tv 800 $2000
a. Identify the decision variables, objective function, and constraints in simple verbal expressions.
b. Mathematically formulate a linear optimization model.