A movie theater in Ellentown, College Cinema, specializes in movies for college students. College Cinema is considered a monopoly in the region, and it serves two groups of moviegoers, LeTall University students and Livayette College students. LeTall students' demand function for movie tickets is QL=20-pL, and Livayette students' demand function is Qv=30-pv. The movie theater incurs zero marginal cost for serving additional customer, but there is a fixed cost of showing a movie at 20. 1. Sum the demand functions of Letall and Livayette students to obtain the total demand function. Then, derive the inverse total demand function. 2. College Cinema is currently charging a uniform ticket price to both groups of students. If the movie theater has been maximizing profit, what are the uniform ticket price and its profit.

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A movie theater in Ellentown, College Cinema, specializes in movies for college students. College Cinema is considered a monopoly in the region, and it serves two groups of moviegoers, LeTall University students and Livayette College students. LeTall students' demand function for movie tickets is QL=20-pL, and Livayette students' demand function is Qv=30-pv. The movie theater incurs zero marginal cost for serving additional customer, but there is a fixed cost of showing a movie at 20.

1. Sum the demand functions of Letall and Livayette students to obtain the total demand function. Then, derive the inverse total demand function. 

2. College Cinema is currently charging a uniform ticket price to both groups of students. If the movie theater has been maximizing profit, what are the uniform ticket price and its profit.

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