The athletic director discussed in the last problem is considering the extra revenue he would gain from three proposals to expand the size of the football stadium. Recall that the demand function he is now facing is given by q (p) = 300, 000 − 10, 000p.
(a) How much could the athletic director increase the total revenue per game from ticket sales if he added 1,000 new seats to the stadium’s capacity and adjusted the ticket price to maximize his revenue?
(b) How much could he increase the revenue per game by adding 50,000 new seats? _______. 60,000 new seats? (The athletic director still wants to maximize revenue.) _____.
(c) A zealous alumnus offers to build as large a stadium as the athletic director would like and donate it to the university. There is only one hitch. The athletic director must price his tickets so as to keep the stadium full. If the athletic director wants to maximize his revenue from ticket sales, how large a stadium should he choose?