Miller Steel is considering purchasing Acme Steel. At present, only the Acme board (not the Miller board) knows the current value of Acme. The Miller board believes that there is an equal chance that Acme is worth either $20 billion or $30 billion. Acme will accept an offer from Miller only if Miller bids at least the current value of the company. For instance, if Acme knows that the company is worth $30 billion, Acme will accept any bid of $30 billion or higher. If and when Miller does purchase Acme, Millers reputation as the largest steel manufacturer will increase the actual value of Acme by 25%.

Suppose that the Miller boards utility function for financial gains or losses x in this operation (in billions of dollars) is given by the square root of (10 + x). Explain what this utility function implies about Miller's risk attitude, and identify Millers optimal decision.