Homer Simpson is very sick and goes to see Dr.Nick Rivera. Without further treatment, Homer will die in about 3 months. The only treatment alternative is a risky operation. Homer is expected to live about 1 year if he survives the operation; however, the probability that a patient will not survive the operation is 0.35. Let U(x) denote Homer’s utility function, where x is the number of months to live. Assuming that U(12) = 1.0 and U(0) = 0, how low can Homer’s utility for living 3 months be and still have the operation be preferred? Justify your answer.