10. Cleaners R Us. offers professional motel room cleaning to motel owners in Danville, Illinois. The company estimates that each additional room it cleans costs the firm $10. The owner's daughter did a study and estimated the firm's demand could be described by the following equation, where P stands for price, and Q for Quantity demanded. She also estimated the marginal revenue equation for the company could be described by the equation below the demand equation. Lastly, since each additional room costs $10 to clean, she also derived a marginal cost equation.
demand	P = $20-$0.01Q (or Q = 2,000 - 100P)
marginal revenue       MR = $20 - $0.02Q
marginal cost	MC = $10
a.	Calculate the output level (Q - number of rooms of rooms cleaned)
at which profits are maximized. (Hint: remember that profits are
maximized at that output where marginal revenue (MR) = marginal
cost (MC))
b.	In order to sell the amount computed in part A. above, at what price
would the company have to offer its service? (Hint: which curve
(equation) gives the relationship between the price of a good or
service and how much of it is demanded?).
c.	What is this firm's total revenue at the optimum price/output computed
in parts A. and B.?