Question: Consider the problem of maximizing the function f(x, y) = 2x + 3y subject to the constraint x + y = 5. (a) Try using

Consider the problem of maximizing the function f(x, y) = 2x + 3y subject to the constraint √x + √y = 5.

(a) Try using Lagrange multipliers to solve the problem.

(b) Does f(25, 0) give a larger value than the one in part (a)?

(c) Solve the problem by graphing the constraint equation and several level curves of f .

(d) Explain why the method of Lagrange multipliers fails to solve the problem.

(e) What is the significance of f (9, 4)?

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