Chapter 4.5, Problem 9E

To determine

The solution of the linear programming problem

Minimize $10x+12y$ subject to the constraints

$\{\begin{array}{c}x+2y\ge 1\\ -x+y\ge 2\\ 2x+3y\ge 1\\ x\ge 0,y\ge 0\end{array}$

and its dual problem with the help of following provided final simplex tableau for the dual,

$\begin{array}{l}uvwxyM\\ \begin{array}{c}x\\ v\\ M\end{array}\left[\begin{array}{lllllll}3\hfill & 0\hfill & 5\hfill & 1\hfill & 1\hfill & 0\hfill & 22\hfill \\ 2\hfill & 1\hfill & 3\hfill & 0\hfill & 1\hfill & 0\hfill & 12\hfill \\ 3\hfill & 0\hfill & 5\hfill & 0\hfill & 2\hfill & 1\hfill & 24\hfill \end{array}\right]\end{array}$