Chapter 4.2, Problem 20E

In Exercises $11-20$, construct the dual problem associated with the primal problem. Solve the primal problem.

Minimize $C=8x+6y+4z$

Subject to $\begin{array}{c}2x+3y+z\ge 6\\ x+2y-2z\ge 4\\ x+y+2z\ge 2\\ x\ge 0\\ y\ge 0\\ z\ge 0\end{array}$