Question 14: Consider an optimization problem \min f(x, y, z, w) = x^…

Consider an optimization problem

$\min f(x, y, z, w) = x^2 + y^2 + z^2 + w^2 + 1$

subject to constraints:

$x + y + z + w = 1$

$w \le \delta$

Let the Lagrangian function is,

$L(x, \alpha, \beta) = x^2 + y^2 + z^2 + w^2 + 1 + \alpha(1 - x - y - z - w) + \beta(w - \delta)$

Based on the above data, answer the given subquestions.