### What is the optimal protection level for full price seat

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(Anneberg) Ron, the director at the Anneberg Center, is planning his pricing strategy for a musical to be held in a 100-seats theatre. He set the full price at \$80 and estimates demand at this price to be normally distributed with mean 40 and standard deviaion 30. Ron also decides to offer students-only advanced sale tickets discounted 50% of the full price. Demand for the discounted student-only ticket is usually abundant and occurs well before full price ticket sells .

a. Suppose Ron sets a 50-seats booking limit for the student-only ticket. What is the number of full price ticket that Ron expects to sell?

b. Based on a review of the show in another city, Ron updates his demand forcast for full price tickets to be normal with mean 60 and standard deviaiton 40, but he doesn't change the prices. What is the optimal protection level for full price seat?

c. Ron realizes that having many empty seats negatively affect the attendees' value from the show . Hence, he decides to change the discount giving on student-only tickets from 50% of the full price to 55% of the full price and he continues to set his protection level optimally. (the demand focusses for full-price ticket remain as in b. normal with mean60 and standard deviation40) How will this change in the student-only discounted price affect the expected number of empty seats? (Will they increase, decrease, or remain the same or it is not possible to determine what will happen?)

d. Ron knows that on average 8 seats (Poison distributed) remain empty due to no-shows. Ron also estimates that it is 10 times more costly for him to have one more attendees than seats relative to having one empty seat in the theatre. What is the maximum number of seats to sell in excess of capacity?

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