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Assume you are the artistic director of a music band that will have a concert in

ID: 357035 • Letter: A

Question

Assume you are the artistic director of a music band that will have a concert in 6 months. The venue reserved for the concert has a capacity of 600 people. You want to sell some tickets in advance at the early-bird price and reserve some tickets for the day of the concert to be sold at the door (at a higher price of course!). Given that you want to maximize the revenue from ticket sales, how many tickets should you sell at the early-bird price, if the early-bird price is $40 and the door-price is $60? Assume the number of customers who prefer to buy their tickets at the door is normally distributed with mean 200 and standard deviation 50. Also assume you can fill up the venue by selling advance tickets but of course that wouldn't generate the highest possible revenue for you. Note: Select the choice that is closest to your answer 421 381 182 0 287 503

Explanation / Answer

In this problem, we need to determine the optimal protection level for full price tickets. If more tickets are reserved than the demand, then $ 40 is lost per ticket reserved for sale at full price, but could not be sold due to no demand for that additional ticket. Similarly, if one less ticket is reserved than demand for full price tickets, then an amount equal to the difference of full price and early bird tickets i.e. 60-40 = $ 20 is lost for every additional unit of demand which could not be met, due to one less ticket reserved for sale on full price.

So, Under-reservation cost, Cu = 60-40 = 20   

Over-reservation cost, Co = 40

Critical ratio = Cu/(Cu+Co) = 20/(20+40) = 0.333

Z = NORMSINV(0.333) = -0.43

Optimal reservation level for full price tickets = Mean demand + z * Std deviation of demand

= 200 + (-0.43)*50  

= 179

Optimal booking level for early bird tickets = 600 - 179 = 421

ANSWER: 421

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