Collector's Sculpture

You are an art collector bidding for a rare sculpture. You know that the value of the sculpture is uniformly at random somewhere between $â¬0$ and $â¬N$ . If your bid is greater than the value of the sculpture, you win and sell it to an art museum at a price of $1.5$ times the true value. What is the optimal price to bid when $N = 1000$ ?

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