Suppose that the production function is given as a function of two inputs, L and K, where L is the quantity of labor and K is the quantity of capital, and expressed as below:

Q=32L-2L2 + 65K-4K2

The price of output is $30 per unit, the price of labor is $95 per unit, and the price of capital is $120 per unit (note, P = 30, w = 95 and r = 120).Answer the followings.

a.Derive the equations for MPL and MPK.

b.Derive the equations for the labor demand function and the capital demand function.

c.Compute the profit maximization level of employment for labor and capital.

d.What is the quantity of output at the profit maximization?

e.Compute the profit.