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.