Question

In: Statistics and Probability

A department store is planning their Spring advertising campaign. They have budgeted $200,000 to use for...

A department store is planning their Spring advertising campaign. They have budgeted $200,000 to use for advertising, and wish to reach the maximum number of potential customers. The advertising firm they are using has carefully obtained the following planning data, to ensure that their client is able to get the most customer impressions possible.

Characteristics	Advertising Medium
Characteristics	Newspaper	Radio	Television
People reached per unit	40,000	120,000	175,000
Number of persons with higher income per unit	25,000	40,000	56,000
Number of married households per unit	20,000	30,000	46,000
Maximum number of ad spots available	150	120	60
Minimum number of ad purchases required	30	40	40
Cost per ad	315	160	1,600

The department store would like to meet the following objectives as a part of its ad campaign:

1) To reach at least 3 million persons in the area.

2) To reach at least 1.3 million persons in the area with above-average income.

3) To reach at least 600,000 married households in the area.

Create a linear programming model that would be used to determine the department store's most effective advertising plan for the next year. Put this into Excel, and using Excel Solver, find the optimal solution for this problem.

Expert Solution

ANSWER::

Solving this linear programming problem using Excel Solver.

Excel setup is done below as shown:

Go to File-> Options-> Excel Add ins -> Solver Add in
Now go to Data -> Solver and setup Solver with decision variables, objective function and constraints.

Click on Solver to get the optimal solution as below:

Hence, department store's most effective advertising plan for the next year is

- Purchase 150 Newspaper,120 Radio and 60 Television ads

- Maximum reach is 30.9 million

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orchestra answered 2 years ago

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