A linear programming problem is to

maximise $4$x$1+2$x$2,$

subject to x$1+$ x$2=12,$ x$1-$x$2,$ x$1,$ x$20.$

$($a$)$ Rewrite the linear program in standard form with three constraints and then add slack variables to write the linear program in equation form.

$($b$)$ Show that a basis that consists of only slack variables gives a basic infeasible solution.

$($c$)$ Introduce an artificial variable x$0$ and solve this problem using either the two$-$phase method or the big M method withthe dictionary format.

$($d$)$ In solving this linear program you would have encountered at least one degenerate basic feasible solution. What was onedegenerate solution? Why is it degenerate?