Explain your reasoning and show calculations$/$steps$,$ please.

This task is known as the feedback vertex set problem.

Consider a graph $G=(V,E)$ with non$-$negative weights $w_v$ for every vertex vinV. We are tasked

with removing a minimal weight subset of vertices of $G,$ such that the remaining graph is acyclical.

a$)$ Write a linear integer program that solves this problem.

b$)$ Develop a primal$-$dual schema to give an approximate solution to the problem.

c$)$ Provide an approximation factor for your algorithm. You might need to modify it$.$