3) Suppose that you have estimated the following output function where L is labor and K is capital:

Y = K^1/4L^1/3

You know that the current price of labor is $123.75 and capital cost is $1 per per machine (capital).

You currently use 81 units (machines) of capital.The price of the output is $40

a)Given a fixed level of capital (K=81), and a price of $40 per unit of output, how many employees (L) will you hire to maximize profit?This requires a calculation.

b)Given a fixed level of capital (K=81), and a price of $40 per unit of output, what is the level of output you will produce?This requires a calculation.

c)Calculate the profit given the optimal number of employees given the answer in #3b.

d)At What number of employees would you maximize output but not lose money?This requires a calculation.