Firm A makes and sells motorcycles. The total cost of each cycle is the sum of the costs of frames, assemble and engine. The form produces its own engines according to the cost equations: CE = 250,000 + 1000Q - 5Q². The cost of frames and assemble is $2,000 per cycle. Monthly demand for cycles is given by the inverse demand equation P = 10,000 - 30Q.
What is the MC of producing additional engine? What is the MC of producing and additional cycle? Find the firm's profit-maximizing quantity and price.