Question

As the marketing manager, you have an advertising budget of $500,000. Several advertising alternatives exist: newspaper, television, radio, and magazine. The information below shows the characteristics associated with each of the advertising alternatives, as well as the maximum number of placements available in each medium. In addition, the total number of print ads (newspaper and magazine put together) should be at least 20. Formulate this as a linear programming problem that maximizes exposure (audience reached).

Type	Cost	Maximum number	Exposure (1000s)
Newspaper	1000	70	60
Magazine	1500	60	50
Television	2000	50	100
Radio	3000	80	70

(a) What are the Decision Variables for the above problem?

Answer:

(b) What is the Objective Function for the above problem?

Answer:

(c) What are the constraints for the above problem?

Answer:

Answer 1

Let the number of newspaper ads be N, magazine ads be M, television ads be T and Radio ads be R.

Hence, the Decision Variables for the above problem are N, M, T, and R.

Based on the given table, the total exposure of all ads = 60,000*N + 50,000*M + 100,000*T + 70,000*R

We have to maximize this exposure. hence, we get objective function as:

Maximize Total Exposure E = 60,000*N + 50,000*M + 100,000*T + 70,000*R

Total Cost of Exposure = 1000*N + 1500*M + 2000*T + 3000*R

Total Budget available = $500,000

Hence,

Subject to Constraints:

1000*N + 1500*M + 2000*T + 3000*R <= 500,000..........Constraint for Budget

N <= 70............................................................................Constraint for max. no. of newspaper ads

M <= 60............................................................................Constraint for max. no. of magazine ads

T <= 50............................................................................Constraint for max. no. of TV ads

R <= 80............................................................................Constraint for max. no. of Radio ads

N + M >= 20.....................................................................Constraint for minimum no. of print ads

M, N, T, R >= 0.................................................................Non-negativity constraint as no. of ads cannot be negative

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