consider the optimization problem: 1 1 min 1 XT XER x + x + 2xy + 3x3 q2 1 1 P23 s.t. x + xy + x3 = 3 Xo - xy + x3 21 XI + Xz - X3 - 5 where Pulls 922,933 are some constants. Consider the point X=[111]'. a) prove or disprove that is a regular point. 6) Find the tangent plane at the point &* . c) write the first-order optimality conditions in order for the point xa to be a local minimum. d) Under the non-degeneracy assumption, write the second-order sufficient condition in order for the point Xe to be a local Minimum, and simplify the condition to obtain an inequality only in terms of qui qur, q33 (without having ox or other unknown parameters). consider the optimization problem: 1 1 min 1 XT XER x + x + 2xy + 3x3 q2 1 1 P23 s.t. x + xy + x3 = 3 Xo - xy + x3 21 XI + Xz - X3 - 5 where Pulls 922,933 are some constants. Consider the point X=[111]'. a) prove or disprove that is a regular point. 6) Find the tangent plane at the point &* . c) write the first-order optimality conditions in order for the point xa to be a local minimum. d) Under the non-degeneracy assumption, write the second-order sufficient condition in order for the point Xe to be a local Minimum, and simplify the condition to obtain an inequality only in terms of qui qur, q33 (without having ox or other unknown parameters)