Professor P has hired a teaching assistant, Mr A. Professor P cares about how many hours that Mr. A teaches and about how much she has to pay him. Professor P wants to maximize her payoff function, x - s, where x is the number of hours taught by Mr. A and s is the total wages she pays him. If Mr. A teaches for x hours and is paid s, his utility is s- c(x)where c(x)= x 2/2. Mr. A's reservation utility is zero. (a) If Professor P chooses x and s to maximize her utility subject to the constraint that Mr. A is willing to work for her, how much teaching will Mr. A be doing