please help

Question 2 (10 points)

Consideraperfectlycompetitivefirmwithshortrunproductionfunctionequaltoq=5 .

a) Call the market price P and the unit wage L and find the expression of the firm's labor demand.

b) Show that if the market price is P = 2 and the unit wage is w = 5 the firm should produce q* = 5 to maximize profit.

c) Now find the firm's short run conditional demand for labor and short run total cost.

d) Suppose the firm had fixed cost FC = 10. In the short run, should it stay open or shut down? Clearly justify your answer.