Q: 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 75% of the time should be allocated to television. Suppose that we have the following data: a) Identify the decision variables, objective function, and constraints in simple verbal expressions. b) Mathematically formulate a linear optimization model. Note: Please clearly state the decision variables, objective function and constraints. The objective function and constraints should be written as a mathematical model using inequality or equality formulas. This question is interested in maximizing the exposure. Type of Ad Exposure/Minute Cost/Minute Radio 350 $400 TV 800 $2,000 P.S: Please solve in Excel by using SOLVER. Please explain what is the optimal solution? What is the resulting output of the objective function at the optimal solution?
Q: 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 75% of the time should be allocated to television.
Suppose that we have the following data:
a) Identify the decision variables, objective function, and constraints in simple verbal expressions.
b) Mathematically formulate a linear optimization model.
Note: Please clearly state the decision variables, objective function and constraints. The objective function and constraints should be written as a mathematical model using inequality or equality formulas. This question is interested in maximizing the exposure.
| Type of Ad | Exposure/Minute | Cost/Minute |
| Radio | 350 | $400 |
| TV | 800 | $2,000 |
P.S: Please solve in Excel by using SOLVER. Please explain what is the optimal solution? What is the resulting output of the objective function at the optimal solution?
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