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.

Use Lagrange multipliers to show that subject to a fixed production level c, the total cost is minimized when

provided Q_x and Q_y are not both P ≠ 0 and and q ≠ 0. 

Qx Qy P 9 and Q(x, y) = c