3. Suppose the costs of a firm in a perfectly competitive market are as follows:

CT=80q+4q^2

Where q is the quantity of goods produced by the firm. In addition, market supply and demand are given by the following inverse equations:

D(P)=6000-3P Demand Function

S(P)=1000+2P Supply Function

1. Find the market equilibrium price
2. Find the equilibrium quantity q, of the perfectly competitive firm that maximizes its profits.
3. Show that this amount maximizes the benefits of the company and graph your result
4. Show the benefits received by the company with the amount of answer B
5. Find the equilibrium quantity Q in supply and demand.