A firm has the production function: F(K,L)=K2/3L1/4, where K is the amount of capital and L is the number of employees. The firm can hire labor at $1 per unit and the price of capital is $1 per unit.

a) Find the cheapest mix of inputs to produce 16 units of output.

b) What returns to scale does this technology demonstrate? Show it analytically.

c) What is the marginal product of labor with small increase in the amount of capital?