Consider the following integer linear programming problem:

max$($x$1+$ x$2),$

$4$x$1+6$x$2+$ x$3=17,$

x$1$ x$2+$ x$4=2,$

xi $>=0,$ x$1,$ x$2$ in Z$.$

Solve $($by hand$)$ the LP relaxation of the problem above starting with

B $=($x$3,$ x$4)$ as a basic feasible solution. Explain what you do$.$

Find $($and explain$)$ a Gomory cut for the optimal solution of the LP

above.