Example: Minimize C = wL+rK Subject to the constraint that a fixed output qo be produced: F(K,L) = AKL = q9o Step 1: Set up the Lagrangian, which is the sum of two components: the cost of production to be minimized and the Lagrange multiplier times the output constraint faced by the firm: - = WL + rK [AKL - 90] Step 2: Differentiate the Lagrangian with respect to K, L, and . Then equate the resulting derivatives to zero to obtain the necessary conditions to a minimum. OF (K,L) (1) =r- =r-(aka-1L) = 0 OF (K,L) (2) = w (BAKL-1) = 0 JL (3) = JL AKLB-90=0