A firm can manufacture a product according to the production function:

Q=F(K,L) =K^3/4L^1/4.

a. Calculate the average product of labor,AP_L, when the level of capital is fixed at 81 units and the firm uses 16 units of labor.

Instruction:Enter your responses rounded to three decimal places.

What is the average product of labor when the firm uses 256 units of labor?

b. Find an expression for the marginal product of labor,MP_L, when the amount of capital is fixed at 81 units.

Instruction:The second response is the exponent onLin the expression. Enter your responses rounded to two decimal places.

MP_L=L^

Then, illustrate that the marginal product of labor depends on the amount of labor hired by calculating the marginal product of labor for 16 and 81 units of labor.

Instruction:Enter your responses rounded to three decimal places.

MP_LwhenL= 16:

MP_LwhenL= 81:

c. Suppose capital is fixed at 81 units. If the firm can sell its output at a price of $200 per unit of output and can hire labor at $50 per unit of labor, how many units of labor should the firm hire in order to maximize profits?

Instruction:Enter your response as a whole number.