A pizza restaurant is trying to figure out how to price Medium and Large pizzas. Customers either come to the restaurant as a couple without children, or as a family with children. Each couple is willing to pay $12 for a Medium pizza or $18 for a Large pizza. Each family is willing to pay $15 for a Medium pizza or $25 for a Large pizza. Couples and families each only ever buy (at most) one pizza. Medium pizzas cost $3 and Large pizzas cost $6 for the restaurant.

Question: Suppose that the restaurant can "directly" price discriminate by charging different prices to couples and to families. What is the profit maximizing way to sell pizza to couples - should a Medium or Large be sold, and at what price?