3. You are approached by the Lucas Museum of Narrative Art, also known as the SIMS. museum. The Museum in seeking to use your unique expertise to update its pricing policy. You nd yourself in a conversation with the creative director, who knows nothing about pricing but wears a green mask with pointy ears and speaks in a strange way. \"Two types of customers, there are,\" he says. \"To the museum once a year Young Padawans go. If a Jedi Master you are, thrice a year attend, you must,\" he continues. He then goes on and on, but and their willingness to pay for that visit is $60, whereas Jedi Masters attend three times a year, and their willingness to pay for all these visits together is $200. It remains unclear how much Jedi Masters would be willing to pay for only one or two visits, but you suspect that the rst yearly visit must be more fun than the second, and the third still less. From a lightsaber-wielding customer service representative you nd more detailed information about current pricing. You can get one-time admission for $50 or yearly membership for $120, and members typically visit the museum three times (conrming your suspicion that these are the Jedi Masters indeed). You then proceed to the meeting room where you would be asked about prot improving pricing strategies. a. A board member proposes increasing the price of one-time admission to $59 (from the current $50). Given what you know about consumer preferences, would you consider this suggestion prot-improving? Or are you lacking the information needed to answer this question? b. Another proposal is to keep the price of one-time admission at $50, but increase the price of yearly membership to $150 (from the current $120). Would you consider this suggestion prot-improving? Or are you lacking the information needed to answer this question? You persuade the board to give you access to data about customers. You nd out that the number of Young Padawans (one-time visitors) is 500,000, and the number of Jedi Masters (who buy membership and visit three times) is 200,000. You also get access to a customer survey and learn that Jedi Masters value the first visit at $120, the second at $50 and the third at $30 (for a total of $200 as you were told before). The marginal cost of each visit is zero. c. Find the profit-maximizing pricing scheme. The Board entertains a plan to make the Museum member-only. In other words, to access the museum, one would have to buy a membership that would allow unlimited access. The Board is condent that Young Padawans will visit the museum only once even if they buy a membership (and Jedi Masters will visit the museum three times). d. How would you price membership? e. How would your answer change if the marginal cost to the museum of an individual's visit is $ 1 0