Consider a firm in a competitive market that has the cost function C(q) = 64q² , where q is the output quantity that the firm produces.

(A) Determine average costs, marginal costs, variable costs and fixed costs.

(B) Calculate the minimum of the average cost function.

(C) Suppose the firm faces price p = 128. Determine the firm's optimal output quantity and its profit at this quantity.

(D) Suppose the firm faces price p = 1. What is the profit if the firm produces q = 0? Is it better for the firm to produce a quantity that is greater than zero than to produce q = 0?