Chapter 6, Problem 15RE

To determine

To calculate: the solution of linear programing problem,

$\text{Minimize }c=x-2y+4z$

$\begin{array}{c}\text{subject to }3x+2y-z\ge 10\\ 2x+y+3z\ge 20\\ x+3y-2z\ge 30\\ x\ge 0,y\ge 0,z\ge 0\end{array}$

by simplex method using technology and if no optimal solution exists, then indicate the feasible region is empty or the objective function is unbounded.