Consider a firm who competes in a perfectly competitive market to produce units of output q. The firm has a cost function TC(q) = 10q4, which means the firm's marginal cost function is MC = 40q. a.) What mathematical condition should be satisfied at the firm's profit-maximizing choice of output? (Write an equation and explain.) b.) If the firm is able to sell for a price of P = 20, what is its profit-maximizing choice of output? What if P = 40? c.) In general, if the firm is able to sell for a general price P , what is its profit-maximizing choice of output? Find a function for qthat depends on P .