You are the CEO of Comchip, a monopoly that sells specialized computers. Each of the firm's computers contains a unique chip that is produced at Comchip's West Coast plant at a cost of C_w(Q_c) = Q_c². Once produced, the chips are shipped exclusively to the firm's East Coast plant. There, the computers are assembled, boxed, and shipped to the market at a cost of C_e(Q) = 200Q. An economic consultant recently estimated the demand for Comchip's computers and found it to be P = 5,000 - Q.

Determine Comchip's optimal output and price for computers, and explain how it can induce plant managers to produce the required number of chips and computers.