2014-63.md

course	course_year	question_number	tags	title	year
Optimization	IB	63	IB 2014 Optimization	Paper 1, Section I, 8H	2014

State and prove the Lagrangian sufficiency theorem.

Use the Lagrangian sufficiency theorem to find the minimum of $2 x_{1}^{2}+2 x_{2}^{2}+x_{3}^{2}$ subject to $x_{1}+x_{2}+x_{3}=1$ (where $x_{1}, x_{2}$ and $x_{3}$ are real).