Given a fixed level of capital and a price of 100 per unit

Question

Please show all work in formulas.

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

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

You know that the current price of labor is $8 and capital cost is $150 per machine (capital).

You currently use 64 units of capital.

For a, the Output (Y) is 100.   

• How many employees (L) do you need to hire to achieve your output goal?
• Given a fixed level of capital (), and a price of $100 per unit of output, what is the optimal number of employees?  You do not need to know Output (Y) for this question.
• Calculate the profit given the optimal number of employee given the answer in b. 
• At What number of employees would you maximize output but not lose money?