Question

Problem 4

Blue ocean insurance services Inc. is working on its advertising strategy and wants to consider four types of media: Internet, Radio, TV, and Newspaper. Their objective is to maximize total exposure to audiences (exposure means number of audiences reached through the ad). The cost of an ad and exposure per ad is provided in the following table:

Media type	Cost per ad	Exposure per ad
Internet	$0.65	300
Radio	$1500	150,000
TV	$5000	350,000
Newspaper	$3500	200,000

The marketing manager has provided you with the following information:

1. Total ad budget should not exceed $100,000
2. Radio and TV must constitute at least 50% of total ads placed.
3. Internet should constitute at least 10% of ads placed.
4. Newspaper should constitute at least 10% of ads placed.

1. Formulate the problem using a linear programming model.
2. Solve your model in Excel, and report the optimal solution. If you get decimals, report them without decimal places (in reality you cannot place fraction of an ad).
3. What is the shadow price for the budget constraint? What does it mean?

Answer 1

Optimal solution is

Media type	Number of ads
Internet	6
Radio	52
TV	0
Newspaper	6

Max Total Exposure

9033815

The Shadow Price of a constraint in Linear Programming indicates how much the value of an objective (optimal) function changes due to a marginal variation in the right-hand side of a constraint. It is assumed that the rest of the model’s parameters remain constant.

So if increase the budget by $ 1 and make it $100,001 the change in total exposure is minimal as below.