Suppose an insurance company would like to design a wellness program for UC Berkeley students to incentivize (or penalize) for their health. For the simplicity of the problem, assume there are two outcomes for health condition: great and non-great. If the student puts any effort for his health condition (e.g. look for traffic before trying to cross a street, drinking responsibly, etc), student's health outcome is great with probability 0.9. Otherwise, if the student puts zero effort to stay healthy, the student's health outcome is great with probability 0.5. The "cost" of the student to put an effort is 10. The utility function of the insurance company satisfies S(great) = 50 and S(not-great) = 10. Suppose the insurance company wants to offer contract to the student, where the student is paid t if the student's health is great, or t otherwise