Nonlinear Programming solution as we found with LINGO. Method for Solving Quadratic Programming Problems method may be used to solve QPPs in which all variables must be nonnegative. illustrate the method by solving the following QPP: min z ” #x1 # x2 $ (%12%)x21 $ x22 # x1x2 s.t. #2×1 $ x2 & 3 s.t. #2×1 # 3×2 & #6 x1, x2 ‘ 0 objective function may be shown to be convex, so any point satisfying the Tucker conditions (36()–(39() will solve this QPP. After employing excess variables x1 constraint and e2 for the x2 constraint in (36(), e(2 for the constraint & #6, and a slack variable s(1for the constraint x1 $ x2 & 3, the K–T conditions be written as # x2 $ )1 # 2)2 # e1 “0 [x1 constraint in (36()] 1 # x1 $ )1 # 3)2 # e2 “0 [x2 constraint in (36()] $ s(1 ” 3 3×2 # e(2″ 6 variables nonnegative 0, )1s(1″ 0, e1x1 ” 0, e2x2 ” 0 that with the exception of the last four equations, the K–T conditions are all linear nonnegativity constraints. The last four equations are the complementary slackness for this QPP. For a general QPP, the complementary slackness conditions may expressed by from xi constraint in (36() and xi cannot both be positive (65) or excess variable for the ith constraint and )i cannot both be positive point satisfying the K–T conditions (except for the complementary slackness Wolfe’s method simply applies a modified version of Phase I of the two-phase ISE 421 -Homework 4 Due by Saturday class time. Solve the following non-linear program: