Consider the following optimization problem:

$(P),$max $x(y^2-z^2)$

$s.t.|y|+z1,$

$xin\{0,1\},z0.$

Answer the questions:

$($a$)$ Is $($P$)$ a linear program, a mixed integer nonlinear program, or a

mixed integer quadratic program? Choose all descriptions that apply.

$($b$)$ Write a minimization problem that is equivalent to $(P).$

$($c$)$ Find all the optimal solutions.