1) This problem deals with the following quadratic programming problem: Minimize X₁ + 5X₂ + 1/2X₂²

Subject to:11< 4

0< X₂< 5

X₁ + 2X₂ = 10

(a) Write this problem in the following vector matrix format: Minimize C^TX + 1/2X^TQX

Subject to: Ax

(b) Write the Lagrangian function for this problem.

(c) Determine the KKT conditions for this problem.

(d) Show that the solution x =(43)^T satises the KKT conditions