The owner of a radio station in a rapidly growing community in central Texas is about to begin operations and must decide what type of program format to offer. She is considering three formats; rock, country, and rap. The number of listeners for a particular format will depend on the type of potential audience that is available. Income from advertising depends on the number of listeners the station has. Three broad categories of audience type can be described as A1, A2, and A3. The rock music format draws mainly for the A1 listener, the country music format draws mainly from the A2 listener and the rap music format draws mainly from the A3 listener. The station owner does not know which type of audience will dominate the community once its growth has stabilized. Probabilities have been

Question

assigned to the potential dominant audience, based on the community growth that has already occurred in this area. Because she wants to begin building an image now, the decision as to which format to adopt must be made in an environment of uncertainty. The station owner has been able to construct the following payoff table, in which the entries are average monthly revenue in thousands of dollars.
Audience
FormatA1
A2
A3
Rock$ 110
$ 80
$ 70
Country$ 90
$ 120
$ 50
Rap$ 70
$ 60
$ 140
Probability0.3
0.5
0.2
What format is optimal? What is the expected profit in that case?

What will be an ideal response?

Answer 1

The expected value of the rock format is ($110)(0.3) + ($80)(0.5) + ($70)(0.2) = $87,000.The expected value of the country format is ($90)(0.3) + ($120)(0.5) + ($50)(0.2) = $97,000.The expected value of the rap format is ($70)(0.3) + ($120)(0.5) + ($50)(0.2) = $91,000.The best course of action with the highest expected value is to select the country format. The expected value of this option is $97,000.