Panther Hall is a college dorm with 100 residents who each have the identical demand function for a pleasant community room, given by the equation MB = 1000 – 9.95Q. The marginal cost of maintaining the community room is MC = 1500 + 5Q, where Q = square footage of the room. The community room is a public good because all dorm residents have open access to the room. The dorm council is considering two plans to maintain the community room: (a) ask residents to voluntarily contribute to the maintenance of the room and (b) add the cost of maintaining the room to the dorm fee for each resident. If the council approves plan a, how much of the community room (in square footage) will each dorm resident be willing to care for on their own? If the council approves plan b, determine the optimal size of the community room and the total amount that each resident pays to maintain the community room?