Bidding on a used machine

A seller privately knows the value $V$ of a used machine, which is uniform on $[0,1]$. You make a single take-it-or-leave-it bid $b$ with $0\le b\le 1$, and the seller accepts exactly when $V\le b$. Because you run the machine better, it is worth $V+\frac{1}{4}$ to you. If the seller accepts, your profit is $V+\frac{1}{4}-b$; otherwise it is $0$. What is your largest possible expected profit? Give the answer as a fraction in lowest terms.

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