A gym is the only seller of personal training sessions in a city of 10,000 people. Each resident's demand for personal training sessions 1s = 10 %p, the marginal revenue is M R(q) = 20 4q. The gym's marginal cost of a training session is $2. a Find the profit maximizing quantity and price 1if the gym acts like a uniform price monopolist b Suppose the gym now charges a fee for joining, f, and a price per training session, p. Find the profit maximizing f and p. How does this number compare to the quantity that maximizes social surplus? d Suppose now the company wants to be like Equinox gyms and adjusts the gym's pricing. Keep the same p as you found in (b), now they decide to charge f=$125. How many training sessions does each person buy at this new scheme and what is the gym's total profit? Explain