A $0-1$ integer linear program is a linear program with the added restriction that each

variable is required to be equal to either $0$ or $1.$ Whereas linear programming is solvable in

polynomial time, no polynomial$-$time algorithm is known for $0-1$ integer linear programming.

Prove that if $0-1$ integer linear programming is polynomial$-$time solvable, then $3-$SAT belongs to $P.$

Hint: Show that the problem of determining whether a given $3-$CNF formula is satisfiable can be

transformed $($in polynomial time$)$ into the problem of determining whether a corresponding $0-1$

integer linear program is feasible.