Suppose a class of 1,000 students is comparing two careers - doctor or lawyer. Let n represent the number who choose to become doctors, so 1, 000  n is the number who choose to become lawyers. Each doctor's income is a function of the number of others who choose to be doctors: p(n) = 250  n/6 (thousands of dollars). Each lawyer's income is a constant s(n) = 150 (thousands of dollars).

(a) Write down the total income to the class as a function of n.

(b) Find the optimal n that maximizes the total income.

(c) How many students choose to become doctors in the Nash equilibrium?