Could you please solve it step by step with clear explanation? Please do not only write the answer. Explanation is very important. I have attached the question below.

(b) (10 points) Consider the following optimization problem: Z = f(.'171,$2) subject to g(x1, x2) = c, Where c is a constant. Write the Lagrangian L for this problem. Show that at the optimum: dz* / dc = X" where A denotes the Lagrange multiplier. Based on this result, What is the interpre- tation of the A