Cost function C(q) = 10 + 10q + q^2 where q is the quantity of laundry services provided.
a. If the price of laundry service is 50 units, how much is the optimal quantity of laundry services to maximize profit and what is the maximum profit that Acme Laundry can achieve?
b. The government noticed that laundry services led to increased water pollution in the nearby river and decided to impose a specific tax of 2 units for every quantity of laundry services provided. How much is the optimal quantity of laundry services to maximize profit and what is the maximum profit that Acme Laundry can achieve with the tax?