Suppose that a monopolist firm faces the demand function:
Q(P) = 60⋅P^(−1/ 2) − 20
and has the cost function: C(Q) = 60(1 - ( 300 / (20 + Q)^2) )
where P is price and Q is output, 0 < P ≤ 9. The firm chooses output
Q ≥ 0 to maximise profit.

a) Write down the firm's profit function as a function of
one variable. Find the output level that maximises profit. Find
the price and the profit at this output level.

b) Find the consumer surplus at the price found in Part
(a). Find the price elasticity of demand at the price found in
Part (a) and interpret the value of the elasticity.

c) Suppose that the government introduces a production
subsidy s per unit of production for the firm so that its profit
function has an additional term s·Q. Find how the profit of
the firm changes as the subsidy increases slightly from 0 (i.e.
find: (dπ(Q*(s))) / ds
at s = 0, where Q*(s) is the solution of the firm's
optimisation problem as a function of the subsidy s, and π is
the firm's profit). Explain your answer.

If someone can help with any of the parts I would really appreciate it. Thanks.