Profits University creates student credit hours (y) with two inputs: Professors' hours of work (x1) and TAs' hours of work (x2) according to the manufacture function: f(x1,x2)= 10x_{1}^{.5}x_{2}^{.25}. Both inputs are variable. Suppose professors are paid $80 per hour and TAs are paid $2.50 per hour. Profits receive $40 per credit hour.
(Profit maximization, both inputs variable)
a) What is the expression for profits as a function of prices and inputs?
b) What is the expression for revenue? For marginal revenue products of every of the inputs?
c) Calculate the two first order conditions for profit maximization. What do they mean?
d) Calculate the inputs and outputs that will maximize Profit's profits. What is the maximum profit that Profits can make?