Profits University produces student credit hours(y) with two inputs:Professors' hours of work(P) and TA's hours of work(T) according to the production function:f(P,T)=10P^(1/2)*T^(1/4). Both inputs are variable. Suppose professors are paid $80 per hour and TAs are paid $2.50 an hour. Profits receive $40 per credit hour. Cost minimization: a) What are the expressions for the marginal product of each of the two inputs in producing credit hours? b) What is the expression for the marginal rate of technical substitution of professors' hours by TA's hours? Interpret MRTS in words. c) Suppose that Profits needs to produce 2000 credit hours this quarter. What is the expression for the respective isoquant? Draw the isoquant. d) What is the minimum cost combination of inputs required to produce 200 credit hours? e) Show that given these input prices, the cost function for profits is C(Y)=120(Y/20)^(4/3)