For each simplex tableau below $(a,b,c)$

a$.$ State the current solution.

b$.$ Explain whether or not the solution for this tableau is in the feasible region.

c$.$ If the solution is feasible, explain how to decide if the solution is an optimal $($best$)$ solution and if the value of $z$ is

maximum.

d$.$ If the solution is feasible but not an optimal solution, find the next pivot and put a box around the number. Show

work that indicates how you chose the pivot.

I.

$\{\begin{array}{ccc}\text{:}[x_1,& x_2,x_3,s_1,s_2,s_3,& s_{4}z]\end{array}$

[62005000361046020406503000120700230063

0-600-5005400]

$0$

$0$

$0$

$0$

$0$

$0$

$0$

$0$

$0$

$\{\begin{array}{ccc}\text{:}[x_1,& x_2,x_3,s_1,s_2,s_3,& s_{4}z]\end{array}$

[1220050004810-8601040621030001267002110063

0300-9001600]

$0$

$0$

$0$

$0$

$0$

$0$

$0$

$0$

$0$

II$.$

$y_1,y_2,y_3,s_1,s_2,s_3,s_4,z$

$\left[\begin{array}{ccccccccc}6& 2& 0& 0& 5& 0& 0& 0& 36\\ 0& 1& 0& 4& 6& 0& 0& 0& 40\\ 0& 6& 5& 0& 3& 0& 25& 0& 75\\ 0& 1& 0& 0& 2& 3& 0& 0& 63\\ 0& 3& 0& 0& 5& 0& 0& 5& 400\end{array}\right]$

III.