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

Y = K^1/4L^1/2

You know that the current price of labor is $10 and capital cost is $1 per per machine (capital).

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

You can either do this using calculus or an excel spreadsheetboth work.If you use calculus, show your work; if you use a spreadsheet, please submit the spreadsheet. Note that number of employees may include fractions (part time workers and product in millions)

1. 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.
2. 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.
3. Calculate the profit given the optimal number of employee given the answer in #3b.

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

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