Reservation price demand

A contract is worth $50$. One buyer arrives and one seller arrives. The buyer's maximum price is $51$ with probability $0.4$, $53$ with probability $0.35$ and $56$ with probability $0.25$. The seller's minimum price is $49$ with probability $0.5$, $47$ with probability $0.3$ and $45$ with probability $0.2$. A buyer trades one unit if the ask is at or below the buyer's maximum, and a seller trades one unit if the bid is at or above the seller's minimum. The market maker picks the ask and the bid to maximize expected profit relative to fair value. What is the maximum expected total profit?

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