An auction house is auctioning a used guitar that is from the 1970s. Given its condition, it can be sold for $10k in the market. There are two other bidders in the auction that we are bidding against, and the guitar goes to the highest bidder. We plan to sell the guitar for $10k upon winning the auction. We believe that the bids of the others are independent and uniformly distributed between $7k and $11k. How much should we bid to maximize our expected profit? (Hint: joint cdfs/pmfs/pdfs may prove useful)