7. (20 min.) Consider the problem: Max. f(x1, x2 ) = -2x2 - 4x2? S.E.X1 + 2x2 2 10 x1.x220 a. Is f a concave function? (Show your work.) Why is this important? b. Find the unconstrained solution. How do you know it's optimal? Explain in words the graphical idea behind how the Gradient Method would find it starting at (1.1): c. Formulate the KKT conditions for this problem (use u's for the dual variables): d. Solve this problem by hand and show your work): e. Briefly explain the idea behind the Modified Simplex method: 7. (20 min.) Consider the problem: Max. f(x1, x2 ) = -2x2 - 4x2? S.E.X1 + 2x2 2 10 x1.x220 a. Is f a concave function? (Show your work.) Why is this important? b. Find the unconstrained solution. How do you know it's optimal? Explain in words the graphical idea behind how the Gradient Method would find it starting at (1.1): c. Formulate the KKT conditions for this problem (use u's for the dual variables): d. Solve this problem by hand and show your work): e. Briefly explain the idea behind the Modified Simplex method