A firm in a perfectly competitive industry has its total cost is given by the equation TC= 100+ q+ q where q is the quantity

A firm in a perfectly competitive industry has its total cost is given by the equation TC= 100+ q²+ q where q is the quantity of output produced by the firm and the market demand for this product is given by the equation P = 1000-2Q where Q is the market quantity. If the market supply curve is given by the equation P = 100+ Q.
i) Determine the equilibrium quantity and price of the market.
ii) Given that the firm's Marginal Cost (MC) equation based upon its Total Cost equation is MC = 2q+1. Determine the firm's profit maximizing level of production, total revenue, total cost and profit at this market equilibrium.
iii) Consider a perfectly competitive market in the short run. Assume that market demand is P=100-4QD and market supply is P=Qs. Denoting firm level quantity by q, assume TC-50+4q+2q² so that MC-4+4q. Determine the number of firms that are in the industry in the short run.