Show me the steps to solve $(15$ points$)$ Let $G=(V,E)$ be an arbitrary directed graph with weighted vertices; vertex weight $w_v$

may be positive, or zero, for all $vinV.$ A prefix of $G$ is a subset of vertices PsubeV such that there

is no edge $uv$ where $u!$inP but vinP. An instance of the Exact $a-b$ Prefix problem consists of

finding a prefix that has exactly a vertices and weights exactly $b.$ In what follows, you may only use

binary variables of the form $x_v$ where $x_v=1$ if vertex vinV is part of the prefix, and $0$ otherwise.

Write the constraints describing a general instance of the Exact $a-b$ Prefix problem. You may only

use basic arithmetic symbols, standard logical operators $,$ etc$),$ and standard set operators

$,$ etc$)$ when defining the constraints.