$($c$)$ Finally, in this part we continue from Question $2$ and matching. Specifically, consider an

assignment problem of $n$ positions to $n$ applicants. Each assignment comes with a cost $c_{ij}>0.$

We want to create a stable matching of minimum cost of positions to applicants. Formulate

the problem mathematically and solve $($using Gurobi$)$ the problem shown in the table below.

You may assume that the costs of assigning job $j$ to applicant i also serve as the preferences $-$

that is$,$ the lower cost, the more they prefer to be assigned. Hence, for example, Applicant $1$

prefers Job $2,$ then Job $1,$ then Job $4,$ and finally Job $3$; whereas Job $2$ prefers Applicant $4,$ then

Applicant $1,$ followed by Applicant $2,$ and then Applicant $3.$ Assume that ties can be broken

arbitrarily.