there is an employer with a single job opening. there are two types of potential employees, good and bad. there are 50% good employees and 50% bad employees in the population. employees know their type, but the employer does not. good (bad) employees have 77% (23%) chance of producing profits gross of compensation of 1,000 and a 23% (77%) chance of producing profits gross of compensation of 500. both type employees have utility for money, w, equal to (w^0.5), that is they are risk-averse. the next best opportunity for a good (bad) employee yields 10(8) in utility. the employer is risk neutral. assume the facts are the same except that there are 97% good employees and 3% bad employ, design the optimal contract that would attract both good and bad employees. how much utility does the bad employee get with this contract? please use mathmatica shows the code program input. thank you