Let a quarry's cost function of producing Q tons of stone per hour be given by TC = Q^{3}- 10Q^{2}+ 40Q + 25, so that marginal cost function is MC= 3Q^{2}- 20Q + 40.
(i) Find the formula for the quarry's short-run supply curve and draw its detailed graph. Explain your solution.
(ii) If market price of a ton of stone is $28, how much will the quarry's manager be willing to produce per hour in the short run? Calculate per hour profit.