linear and quadratic problem.

The daily demand for rooms at a motel is given by , where P is the price of a room and Q is quantity demanded for rooms. Assume that the motel has 40 rooms.

5a. If total variable costs of running this motel are zero, find the price that maximizes profit and find the number of rooms rented at that price. Remember that profit is total revenue (i.e., TR = PQ) less total cost (i.e., the sum of variable costs and fixed costs).

5b. If the incremental cost of renting a room is $9 (i.e., the cost of paying the maid to clean the room, the cost of providing clean towels, the cost of the little pieces of chocolate that is placed on the bed, etc. is $9), find the price that maximizes profit and the number of rooms rented at that price.

Professor said Total Variable is 0 but total fixed is unknown

I got as far as TR=PQ

TR=PQ= (100-2Q)Q

TR=PQ=100Q-2Q²

^{The prof walked us through the basics for part A and part B}

D P= 100 - 291 Problem 5 A TR = P. Q = ( 100 - 24 ) 9 = 10VQ - 242 TI= TR - TC IT =( 1004- 2427 - T FVe+ THE Rooms Rented TVC TVE - 9q Problems $9 - $94 B F18 31$27 TVC = 94