A linear programming problem is to

maximise $4x_1+2x_2,$

subject $to{x}_1+x_2=12,$

$x_1-x_{2}2,$

$x_1,x_{2}0.$

$($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 xo and solve this problem using either the two$-$phase method or the big M method with the dictionary format.

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