Chapter 4.1, Problem 24E

(a) Name the group I and group II variables in the tableau as given

$\begin{array}{l}xyuvwM\\ \left[\begin{array}{cccccc}1& 2& 1& 0& 0& 0\\ 1& 1& 0& 1& 0& 0\\ 2& 1& 0& 0& 1& 0\\ -9& -5& 0& 0& 0& 1\end{array}|\begin{array}{c}15\\ 27\\ 42\\ 0\end{array}\right]\end{array}$

(b) Pivot the simplex tableau about each indicated element, and compute the solution corresponding to the new tableau. Which solutions are feasible (that is, have all values $\ge 0$)? Which variables are now in group I; which are in group II?

(i) 1 (row 1, column 1)

(ii) 2 (row 1)

(iii) 2 (row 3)

(iv) 1 (row 3, column 2)

(c) Which of the feasible solutions increases the value of M the most?