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AMC theater is a local monopolist of movies. AMC faces two types of customers: regular (R), and colleague students (S). The demand function for regular customers is qR = 15 - 0.5P, while the demand function for students is qS = 10 - 0.4P. AMC's cost function is C(q) = 10q.
(a) Suppose AMC can distinguish the type of customers by checking their IDs. Find AMC's maximal profit if it sets the different prices for different types of customers.
(b) Suppose AMC is not allowed to check ID and therefore has to set a single price for both types of customers. Find AMC's maximal profit.
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