A linear programming problem is to

$mamise4x_1+2x_2,$

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

$x_1-x_{2}2,$

$x_1,x_2,x_{3}0.$

$($a$)$ Rewrite the linear program in standard form with three con

straint and then add slack variables to write the linear pro$-$

gram 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 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?