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Consider the following problem:maximize (minimize) 3x + y subject to the constraints: 4x-3y= 9 and x + z = 9(a) Write down the Lagrangian function.(b)

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Consider the following problem:maximize (minimize) 3x² + y subject to the constraints: 4x-3y= 9 and x² + z² = 9(a) Write down the Lagrangian function.(b) What are the first-order conditions?(c) Find the solutions for the given problem.

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