Suppose the owner of the only bowling club in town wants to determine his profit under the two-part rate scheme. To do t

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Suppose the owner of the only bowling club in town wants todetermine his profit under the two-part rate scheme. To do this, hehas identified two types of consumers, professionals and amateurs.The demand function of the first and second groups are: q1 = 100 –p, q2 = 50 – 1⁄2 p. The costs of the bowling club are given by: CT= 20q (2.0 points).a. Find the equilibrium price, the quantity offered to each type ofconsumer, the rate, and the total benefit.b. Graph each group's demand, costs, and breakeven.c. Now suppose that the owner wants to evaluate the benefit that hewould obtain under the third degree discriminating monopoly scheme,if he can maintain the separation of markets, how much does heoffer to each type of consumer and at what price?what is your benefit? Does the law of inverse elasticity hold?Why?d. Graphically represent the equilibrium under the scheme of theprevious paragraph.and. Explain which of the two options suits the owner and why.