Use the Simplex Method to Solve the Linear Programming Problem $\mathrm{z}=4 \mathrm{x}_{1}+2 \mathrm{x}_{2}$

Use the simplex method to solve the linear programming problem.
-Maximize $\mathrm{z}=4 \mathrm{x}_{1}+2 \mathrm{x}_{2}$
Subject to: $2 x_{1}+3 x_{2} \leq 6$
$x_{1}+3 x_{2} \leq 4$
$2 \mathrm{x}_{1}+2 \mathrm{x}_{2} \leq 8$
With $\quad x_{1} \geq 0, x_{2} \geq 0$

A) Maximum is 6 when $x_{1}=0, x_{2}=3$
B) Maximum is 8 when $x_{1}=0, x_{2}=2$
C) Maximum is 16 when $x_{1}=4, x_{2}=0$
D) Maximum is 12 when $\mathrm{x}_{1}=3, \mathrm{x}_{2}=0$