Question: Consider the following optimisation problem: minimize fo (x) = (x1 2)2 + 4(x2 6)2 subject to f1 (2) = 1241 + 6(x2 + 1) =

Consider the following optimisation problem:

Consider the following optimisation problem: minimize fo (x) = (x1 2)2 + 4(x2 6)2 subject to f1 (2) = 1241 + 6(x2 + 1) = 16 Xi = 12 Xi > 0 = 12 > 0 1. Visualise the problem (plot the functions on the x1-x2 plane). 2. Find the optimal solution visually. Which constraints are binding? What can you say about the Lagrange multipliers associated with the constraints that are not binding? [0.5 point] 3. Solve the optimisation problem using the KKT conditions. Use the solution from the previous step as a guidance when eliminating candidate complementary slackness solutions! [1 point]

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