A local golf course's hired-gun econometrician has determined that there are two types of golfers, frequent and infrequent. Frequent golfers' annual demand for rounds of golf is given by Q-= 24 -0.3P, where P is the price of a round of golf. In contrast, infrequent golfers' annual demand for rounds of golf is given by Q = 10 - 0.1P. the marginal and average total cost of providing a round of golf is $20. a. If the course wishes to maximize profit, what price should it establish for the discounted plan? b. If the course wishes to maximize profit, what minimum quantity should it establish for the discounted plan? c. Which plan will generate the greatest consumer surplus for frequent golfers? d. Which plan will generate the greatest consumer surplus for infrequent golfers? e. Based on your answers to (g) and (h), will the plan be successful in making golfers self- select into the most profitable plan for the golf course? f. Suppose that each type of golfer came to the course with the word "frequent" or "infrequent" tattooed on his or her forehead. Is this information of any value to the golf course owner? (In other words, can the owner earn any more profits by segmenting than it did with its quantity discount plan?)