The owner of a radio station in a rapidly growing community in central Texas is

Question

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 assigned to the potential dominant audience, based on the community growth that has already occurred in this area. Since 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.

What is the expected profit in that case?

Format A1 A2 A3 Rock 110$ 80$ 70$ Country 90$ 120$ 50$ Rap 70$ 60$ 140$ Probability 0.3 0.5 0.2

Explanation / Answer

We have to select the format with high expected value

E(Rock) = 110*0.3 + 80*0.5 + 70*0.2 = 87 = 87,000$

E(Country) = 90*0.3 +120*0.5 + 50*0.2 = 97 = 97,000$

E(Rap) = 70*0.3 + 60*0.5 + 140*0.2 = 79 = 79,000$

Clearly from above country format has high expected value

so Country format is to be decided

Expected profit = $ 97,000

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