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A restaurant has three types of customers. A third of its customers, Type A, are willing to spend $5 on an appetizer but only

 

A restaurant has three types of customers. A third of its customers, Type A, are willing to spend $5 on an appetizer but only $2 on a dessert. Another third, Type B, are willing to spend $3.50 on an appetizer and $3.50 on a dessert. The remaining third, Type C, are willing to spend only $2 on an appetizer but $5 on a dessert. All three types are willing to spend $10 on the main course. It costs the restaurant a constant $2 to prepare an appetizer or a dessert, and $7 to prepare the main course. Which is optimal for the restaurant, to offer appetizers and desserts la carte (with separate prices on the menu), or to offer them only as a complete meal, tied in with the main course?

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