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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

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.

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(b) (10 points) Consider the following optimization problem: Z = f(371, 392) subject to 9(231, 21:2) 2 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

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