Optimization in economic question?

A firm that produces a single product faces a demand function : q = 10,000P - 100P where q is the quantity demanded, and p is the firm’s price. Its total cost function is : TC(q)= 200+20q+q2/300.

the question is : What is the profit-maximising level of production for this firm? answer= q=3000

What is the firm’s maximum profit? R= 119800

Calculate (discrete) marginal revenue and (discrete) marginal cost at an output of 2000 ?. MR=60 , Mc= 33.3

The correct answers are in brackets after the question , but I am more interested in explaining how the answer was obtained. with thanks

Re: Optimization in economic question?

(Hint) Write a formula for profit (π) in terms of q

Re: Optimization in economic question?