Problem $7$: a$)$ Write with your favorite software a linear program that takes in input a number $\backslash ($ n $\backslash )$ of buyers, $\backslash ($ m $\backslash )$ of sellers, and their valuations, and outputs an equilibrium to the problem. Create $50$ random instances with $\backslash ($ n$=10,$ m$=20\backslash )$ and compute the corresponding equilibria.

b$)$ Write code that decides, for an instance of the assignment game as in part a$),$ if there is another equilibrium for the instance $($i$.$e$.,$ one different from the one you have already found$).$ Your code should solve one or more linear programs.