Your private equity firm is considering making an offer to buy a small yogurt firm with the intent of reselling it after streamlining its operations. The problem is that you don’t know the exact current value of the firm. You are sure that it is equally likely to be worth anywhere in the range of $150 million to $600 million dollars (a uniform distribution). You also know that if your offer exceeds the value of the firm the current owners will sell. Given your track record of enhancing the value of existing firms, you are confident that you can increase the value of the firm by $50 million. What is the highest offer you can make without expecting to lose money on average?