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Suppose we want to maximize the utility function u = x 2 y subject to the following two constraints: x + y 100 and 2
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.
1.Write the Lagrangian function L.
2.Write the Kuhn-Tucker conditions for this problem.
3.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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