Chapter 4.4, Problem 6E

(a)

To determine

To calculate: The solution of a minimization problem, using $y_1,y_2,y_3$ as the variable and $g$ as function whose final simplex table is given as,

$\left[\begin{array}{rrrrrrrr}\hfill 0& \hfill 0& \hfill 1& \hfill \frac{2}{5}& \hfill \frac{5}{3}& \hfill \frac{4}{15}& \hfill 0& \hfill 16\\ \hfill 1& \hfill 0& \hfill 0& \hfill \frac{-1}{5}& \hfill \frac{11}{3}& \hfill \frac{1}{5}& \hfill 0& \hfill 19\\ \hfill 0& \hfill 1& \hfill 0& \hfill \frac{3}{5}& \hfill \frac{-2}{3}& \hfill \frac{2}{3}& \hfill 0& \hfill 22\\ \hfill 0& \hfill 0& \hfill 0& \hfill 12& \hfill 15& \hfill 20& \hfill 1& \hfill 554\end{array}\right]$

(b)

To determine

To calculate: The solution of the maximization problem, using $x_1,x_2,x_3$ as the variable and $f$ as a function where the final simplex table of a minimization problem is provided as,

$\left[\begin{array}{rrrrrrrr}\hfill 0& \hfill 0& \hfill 1& \hfill \frac{2}{5}& \hfill \frac{5}{3}& \hfill \frac{4}{15}& \hfill 0& \hfill 16\\ \hfill 1& \hfill 0& \hfill 0& \hfill \frac{-1}{5}& \hfill \frac{11}{3}& \hfill \frac{1}{5}& \hfill 0& \hfill 19\\ \hfill 0& \hfill 1& \hfill 0& \hfill \frac{3}{5}& \hfill \frac{-2}{3}& \hfill \frac{2}{3}& \hfill 0& \hfill 22\\ \hfill 0& \hfill 0& \hfill 0& \hfill 12& \hfill 15& \hfill 20& \hfill 1& \hfill 554\end{array}\right]$