Suppose your firm's production function is given by: F(L,K)=K 1/2 L 1/4 You also know that the wage rate for labor w=$200, the price of capital...

Suppose your firm's production function is given by: F(L,K)=K1/2L1/4

You also know that the wage rate for labor w=$200, the price of capital r=$100. 

a.) In the short-run, capital is fixed at 81 units. How many units of Labor should the firm hire in order to maximize profits/minimize costs if it can sell its product for $19,200?  

b.) In the short-run, based on your answer from a., how many units of output does the firm produce? 

c.) In the