A marketing manager is trying to determine the advertising mix for a new product. Three types of ads are being considered: radio, TV and newspaper. The firm's ad agency has provided the following data:
|
Type of ad
|
Radio
|
TV
|
Newspaper
|
|
Cost per ad
|
$1900
|
$3000
|
$1400
|
|
Number of customers exposed per ad
|
35,000
|
70,000
|
50,000
|
|
Number of units sold per ad
|
3,000
|
8,000
|
5,000
|
Several other criteria must be met: the advertising budget is $100,000, total exposure must be 2,500,000 customers, and no more than 30 ads may appear in any medium. The firm wants to maximize total number of units sold.
Write the LP formulation, set the problem up in Excel and use Solver to find the optimal solution
Use your Solver output to answer the questions below.
A. What is the optimal solution and the total number of units sold?
B. Within what range can the objective function coefficient for newspapers vary without changing the optimal solution?
C. What would the number of units sold per radio ad have to change to in order for radio ads to be used in the advertising mix?
D. What would marginal benefit of adding to the advertising budget be? How high could we increase the budget and still expect this benefit?
E. If we didn't restrict the number of newspaper ads, how many could we allow before the optimal solution would change?
F. Would the solution change if the number of units sold per ad changed to the values in the following table?
Radio TV Newspaper
No. of units sold per ad 3500 10000 4500