# solution

Consider a parking lot in a community near Manhattan. The parking lot has 100 parking spaces. The parking lot attracts both commuters and daily parkers. The parking lot manager knows that he can fill the lot with commuters at a monthly fee of \$180 each. The parking lot manager has conducted a study and has found that the expected monthly revenue from x parking spaces dedicated to daily parkers is approximated well by the quadratic function R(x) = 300x-1.5x^2 over the range of x in {0, 1, …, 100}.Note: Assume for the purpose of the analysis that parking slots rented to commuters cannot be used for daily parkers even if some commuters do not always use their slots. (a)What would the expected monthly revenue of the parking lot be if all the capacity is allocated to commuters? (b)What would the expected monthly revenue of the parking lot be if all the capacity is allocated to daily parkers? (c)How many units should the parking manager allocate to daily parkers and how many to commuters? (d)What is the expected revenue under the optimal allocation policy?