Tianyu sells coffee in the City of Berkeley. The coffee market can be considered perfectly competitive since there are many coffee suppliers like Tianyu and many consumers such as Berkeley students. The long-run total cost of coffee production is TC=q^3 - Sq^2 + 20q and the corresponding marginal cost is MC = 3q^2 - 16q + 20 where qq denotes the cups of coffee Tianyu produces. The market demand for coffee is QD= 1000-150P and the current market supply is QS = 200P-400. Find the optimal coffee production for Tianyu and the corresponding profit. Show your calculation details.