Consider the following linear programming problem: $(30$ points$)$

$($a$)$ Use the graphical method to find the optimum solution.

$($b$)$ Work through the simplex method step by step $($in tabular form$)$ to determine the optimum

solution.

$($c$)$ What are the basic variables and basic feasible solution at each iteration of the simplex

method? State the corner point feasible solution, obtained from the graphical solution in problem

part $($a$),$ corresponding to each basic feasible solution