In Exercises 28 through 30, let Q(x, y) be a production function, where x and y represent

Question:

In Exercises 28 through 30, let Q(x, y) be a production function, where x and y represent units of labor and capital, respectively. If unit costs of labor and capital are given by p and q, respectively, then px + qy represents the total cost of production.

Show that with the fixed production level Ax^αy^β = k, where k is a constant and α and β are positive with α + β = 1, the joint cost function C(x, y) = px + qy is minimized when