Stone Co. is the only automobile producer in Orange County.

Stone Co. is the only automobile producer in Orange County. The market demand for automobiles in Orange County is given by P = a-bQ, where a and b are positive constants, P denotes market price and Q denotes the number of automobiles purchased by customers. Stone Co. has a cost function C(q) = cq where c is a constant and q denotes the amount of output produced by Stone Co. Assume a>c>0 and b>0.Write down the optimization problem for the Stone Company. Then determine the amount of output produced by Stone Company. How much profit will Stone Company make when it acts as a monopolist?