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

Suppose that you have estimated the following output function where L is labor and K is capital: Y = K1/4L1/2   

You know that the current price of labor is $10 and capital cost is $150 per machine (capital).
You currently use 81 units of capital.
For #3a, the Output (Y) is 100

Using calculus, Please show all work in order to understand where things are coming from. Thank you.
  
a.How many employees (L) do you need to hire to achieve your output goal?


b. Given a fixed level of capital (K=81), and a price of $100 per unit of output, what is the optimal number of employees?


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


d. At What number of employees would you maximize output but not lose money?

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