Chapter 4.3, Problem 14E

(a)

To determine

The values of all the variable and the objective function f.

The given matrix is

$\left[\begin{array}{cccccccc}5& 5& 7& 1& 0& 0& 0& 12\\ 4& 0& 6& 0& 1& 0& 0& 48\\ 0& 1& 1& 0& 0& 1& 0& 8\\ -1& -3& -1& 0& 0& 0& 1& 0\end{array}\right]$

(b)

To determine

Whether the solution of (a) is optimal or not.

The given simplex matrix is

$\left[\begin{array}{cccccccc}5& 5& 7& 1& 0& 0& 0& 12\\ 4& 0& 6& 0& 1& 0& 0& 48\\ 0& 1& 1& 0& 0& 1& 0& 8\\ -1& -3& -1& 0& 0& 0& 1& 0\end{array}\right]$

(c)

To determine

The next pivot and state all the row operation on that pivot for the given matrix.

The given simplex matrix is

$\left[\begin{array}{cccccccc}5& 5& 7& 1& 0& 0& 0& 12\\ 4& 0& 6& 0& 1& 0& 0& 48\\ 0& 1& 1& 0& 0& 1& 0& 8\\ -1& -3& -1& 0& 0& 0& 1& 0\end{array}\right]$