Chapter 4.3, Problem 15E

(a)

To determine

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

The given matrix is

$\left[\begin{array}{cccccccc}1& 4& 0& 0& \frac{3}{4}& 4& 0& 24\\ 0& -2& 0& 1& \frac{-5}{8}& -2& 0& 16\\ 0& 3& 1& 0& 2& 6& 0& 21\\ 0& 4& 0& 0& 2& \frac{1}{2}& 1& 780\end{array}\right]$

(b)

To determine

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

The given simplex matrix is

$\left[\begin{array}{cccccccc}1& 4& 0& 0& \frac{3}{4}& 4& 0& 24\\ 0& -2& 0& 1& \frac{-5}{8}& -2& 0& 16\\ 0& 3& 1& 0& 2& 6& 0& 21\\ 0& 4& 0& 0& 2& \frac{1}{2}& 1& 780\end{array}\right]$