2) Suppose that you have estimated the following output function where L is labor and K is capital: Y = 2K^1/4L^1/2 You know that the current price of labor is $10 and capital cost is $1 per machine (capital). You currently use 81 units (machines) of capital. The price of the output is $40.

Note that number of employees may include fractions (part-time workers and product in millions)

a) Given a fixed level of capital (K=81), and a price of $40 per unit of output (output is represented by Y), 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 #2b.

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

e) If the Wage Rate Rose to $12.50, what would be the possible outcomes to L, P, and Profit?