WVTU is a television station that has 20 thirty-second advertising slots during its regularly scheduled programming each evening. The station is now selling advertising for the first few days in November. It could sell all the slots immediately for $4,500 each, but because November 7 will be Election Day, the station manager knows she might be able to sell slots at the last minute to political candidates in tight races for $8,000 each. The demand for these last minute slots is estimated as follows:

Slots not sold in advance and not sold to political candidates at the last minute can be sold to local advertisers for $2,000.
a. If the station manager sells all the advertising slots in advance, how much revenue will the station receive?
b. How many advertising slots should be sold in advance if the station manager wants to maximize expected revenue?
c. If the station manager sells in advance the number of slots identified in the previous question, what is the probability that the total revenue received will exceed the amount identified in part a where all slots are sold inadvance?

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Demand 8 9 10 1 12 13 14 15 16 17 18 19 Probability 0.03 0.05 0.1005 020 0.15 0.10 0.05 0.05 0.05 0.05 0.02