Question

Find the maximum value of = √ subject to the cost constraint K + 4L = 16.

Estimate the change in the optimal value of Q if the cost constraint is changes to K +
4L = 17

Answer 1

This problem can be solved using the method of Lagrange multipliers. Let's define the Lagrangian function as: L(K, L, λ) = Q - λ(K + 4L - 16) Taking partial derivatives with respect to K, L, and λ, we get: dL/dK = 0 => 1 - λ = 0 => λ = 1 dL/dL = 0 => 1 - 4λ = 0 => λ = 1/4 dL/dλ = K + 4L - 16 = 0 Solving the last equation for K, we get: K = 16 - 4L Substituting this into the Lagrangian function, we get: L = Q - λ(16 - 4L + 4