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?