Problem 2. Hair salon versioning. A local hair salon in New Haven is re-designing its business...

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Problem 2. Hair salon versioning. A local hair salon in New Haven is re-designing its business plan. The owner has discovered that they can make more money by offering two packages: "Deluxe" and "Basic". There are two types of customers: Type A customers usually only need to get haircuts, while Type B customers would enjoy other services (wash, conditioning, coloring, ironing, etc.). Suppose that there are 4 type A customers for each type B customer. The reservations values for each type and marginal costs for each version are as follows: Basic (MC=20) Reservation Values: Deluxe (MC=50) Type A (4) $30 $60 Type B (1) $60 $90 The optimal menu has the form of: Get the basic package for pg dollars, or get the deluxe package for pp dollars. a) What are the constraints that will bind under this menu? b) Use the answers in part a), find the prices pg and pp. c) What is the hair salon's profit by offering this menu? d) What is the hair salon's profit if it only serves type B by offering the deluxe package only? Problem 2. Hair salon versioning. A local hair salon in New Haven is re-designing its business plan. The owner has discovered that they can make more money by offering two packages: "Deluxe" and "Basic". There are two types of customers: Type A customers usually only need to get haircuts, while Type B customers would enjoy other services (wash, conditioning, coloring, ironing, etc.). Suppose that there are 4 type A customers for each type B customer. The reservations values for each type and marginal costs for each version are as follows: Basic (MC=20) Reservation Values: Deluxe (MC=50) Type A (4) $30 $60 Type B (1) $60 $90 The optimal menu has the form of: Get the basic package for pg dollars, or get the deluxe package for pp dollars. a) What are the constraints that will bind under this menu? b) Use the answers in part a), find the prices pg and pp. c) What is the hair salon's profit by offering this menu? d) What is the hair salon's profit if it only serves type B by offering the deluxe package only?