You are hoping to take advantage of an opportunity to operate a small business this summer. In order to provide your services to potential customers, you will need to hire one worker. If you hire a "hard-working" employee, you will make $5,000 in profit. If you end up with a "lazy" employee, you will only make $1,000 in profit. There is an 80 percent chance that you will hire a "hard-working" employee and a 20 percent chance that you will hire a "lazy" employee. Suppose you have a utility function of the form u=x^3/4, where X is the amount of profit you make.(a) What is your expected utility this summer?(b) Cindy is an employment consultant and an infallible judge of talent and character. After an interview, she can state with certainty whether the worker will be "hard-working." Would you be willing to pay her $1,000 for her services? Explain.(c) What is the maximum amount you would be willing to pay Cindy?