A Hard Economics Question?

[briv]

Koolworks is producing its product in a competitive market which means that it is a price-taking firm. The market demand curve and the supply curve for Koolworks’ product are given below.

Demand curve:Qd = 5,000 – 10 P
Supply Curve: Qs= 40 P
Koolworks faces the following total cost function: TC = 20 Q + 2 Q2 . The marginal cost curve of this firm is as follows: MC = 20 + 4 Q.
(a)Determine the profit maximizing output for Koolworks under the given conditions.
(b)Determine the amount of profit that Koolworks will earn at this level of output.
(c)Suppose that all the other firms in this market also have identical cost conditions as does Koolworks. How many firms are there in this market?
(d)Suppose that Koolworks now face $300 as the fixed costs so that its total cost function changes to: TC = 300 + 20 Q + 2 Q2 . What will be profit maximizing output for Koolworks with this new TC function? What will be the new maximum profit that Koolworks will earn with this new TC function?