Cost Minimization

Suppose an organization wants to produce 100 units of output at the lowest possible cost. The price of capital is $50 and the price of labor is $20 and the organization has the following production function:

Q = K^0.4 L^0.6

How much capital and labor should it use? What will be its average cost per unit of output at this set of inputs? You may assume that the organization can buy fractional amounts of labor. As a hint to reduce the number of calculations you'll need to do, the amount of capital is between 40 and 50 inclusive.

Solution