1.I.8COptimizationPart IB, 2006State the Lagrangian sufficiency theorem.Let p∈(1,∞)p \in(1, \infty)p∈(1,∞) and let a1,…,an∈Ra_{1}, \ldots, a_{n} \in \mathbb{R}a1,…,an∈R. Maximize∑i=1naixi\sum_{i=1}^{n} a_{i} x_{i}i=1∑naixisubject to∑i=1n∣xi∣p⩽1,x1,…,xn∈R\sum_{i=1}^{n}\left|x_{i}\right|^{p} \leqslant 1, \quad x_{1}, \ldots, x_{n} \in \mathbb{R}i=1∑n∣xi∣p⩽1,x1,…,xn∈R