A brand manager for ColPal Products must determine how much time to allocate bet

Question

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: a. Identify the decision variables, objective function, and constraints in simple verbal expressions. b. Mathematically formulate a linear optimization model.

Explanation / Answer

Let x be the time in minutes to be allocated for Radio ads and
y be the time in minutes to be allocated for TV ads

Here the objective is to maximize the exposure
Exposure = 350x + 800y

Constraints are
1) Budget constraint states that total ad expense should not exceed $25000,
400x + 2000y <= 25000

2) Time constraint states that time allocated to TV ads, y is greater than equal to the total time allocated (x+y),
y >= 0.7(x+y) i.e. -0.7x + 0.3y >= 0

Mathematical formulation
Maximize Z = 350x + 800y
subject to,
400x + 2000y <= 25000
-0.7x + 0.3y >= 0

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