Consider the following production function : Q = 10L²K, where Q is the amount of production,L is the amount of Labor and K is the amount of Capital.

a. Does this production function exhibit the law of diminishing returns ? Explain.

b. Does this production function exhibit diminishing return to scale ? Explain.

c. If the price of labor is 1 dollar per unit and the price of capital is 5 dollars per unit, how much labor and capital should this firm optimally hire ?

Hint 1 : total budget is 150,000 dollars

Hint 2 : marginal product of labor is 20LK.

Hint 3. marginal product of capital is 10L².