WVTU is a television station that has 20 thirty-second advertising slots during
ID: 465475 • Letter: W
Question
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.
QUESTIONS
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 in advance?
*** Formulas in Excel cells are critical to understanding the answer and learning. Please attached Excel file or Screenshots that show formulas. ***
Demand Probability 8 0.03 9 0.05 10 0.10 11 0.15 12 0.20 13 0.15 14 0.10 15 0.05 16 0.05 17 0.05 18 0.05 19 0.02Explanation / Answer
A. If all slots are sold at once Revenue =20*4500 90000 B. If we assume demand is met the number of sold and unsold in each case would be as shown. Sold Probability Unsold Probability of being Unsold Expected Revenue s p u up s*p*8000+u*up*2000 8 0.03 12 0.97 25200 9 0.05 11 0.95 24500 10 0.1 10 0.9 26000 11 0.15 9 0.85 28500 12 0.2 8 0.8 32000 13 0.15 7 0.85 27500 14 0.1 6 0.9 22000 15 0.05 5 0.95 15500 16 0.05 4 0.95 14000 17 0.05 3 0.95 12500 18 0.05 2 0.95 11000 19 0.02 1 0.98 5000 As highlighted, the maximum revenue of $32000 happens when 12 slots are sold at 8000$ and remaining are sold at 2000$ C. Sorry about third part of question. I am somewhat doubtfull about the data provided.So not going with the solution part.
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