Please solve step by step! Thanks!

The company owns the rights to a mine containing B = 2000 tons of ore. If the ore is mined at a rate of q (tons/month), the revenue generated from the sale of ore is R(q) = 85q-0.25q^2 (?/month), and the cost incurred from the operation is C(q) = 250+10q+0.50q^2 (?/month):

(a) Maximize the company's monthly profit.

(b) Maximize the company's profit when it mines all the ore.

(c) Determine the following integral, which is the present value of the cash flow when the continuous interest rate is 12.75%.