Hannah is the owner of the Regent Theater in the small rural town of Eureka.

Question 2 [25 pomts) 2. Hannah is the owner of the Regent Theater in the small rural town of Eureka. The Regent is the only theater in the county and is the main entertainment in the area. The demand for the Regent is Q = 400 501D , and TC = 5Q + 215622, where P is the price of admission and Q is the number of admissions per day. (a) What price and output will Hannah choose if she maximizes prot? (7 points) (b) Hannah decides to leave Eureka and hires her nephew to manage the Regent. The nephew is ambitious and believes that he can increase business at the Regent. What price and output should he pick to maximize revenue? (7 points) (c) Hannah is impressed to learn that her nephew has increased admissions, but she is concerned that the theater is now not making enough money every day. She tells her nephew that she will re him unless the rm at least breaks even. What price and output will the nephew pick to make sure that prots are equal to zero? (Hint: this rm is not a price-taker; just make sure that prots are equal to zero.) (9 points)