Problem 18. Suppose we want to maximize the utility function u = x2y subject to the...

Problem 18. Suppose we want to maximize the utility function u = x²y subject to the following two constraints: x + y ≤ 100 and 2x + 8y ≤ 240. Also, x and y must be greater than or equal to 0.

Write the Lagrangian function L.
Write the Kuhn-Tucker conditions for this problem.
Use trial and error to solve for the optimal values of x and y. What are the values of the Lagrange multipliers at the optimal solution?. Be sure to explain what you are doing in each step.

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