Use the Two-Stage Method to Solve $\mathrm{z}=3 \mathrm{x}_{1}+2 \mathrm{x}_{2}$ Subject To $\mathrm{x}_{1}+\mathrm{x}_{2}=5$

Use the two-stage method to solve.
-Maximize $\mathrm{z}=3 \mathrm{x}_{1}+2 \mathrm{x}_{2}$
Subject to: $\mathrm{x}_{1}+\mathrm{x}_{2}=5$
$4 \mathrm{x}_{1}+2 \mathrm{x}_{2} \geq 12$
$5 x_{1}+2 x_{2} \leq 16$
$x_{1} \geq 0, x_{2} \geq 0$

A) Maximum is 12 for $\mathrm{x}_{1}=2, \mathrm{x}_{2}=3$
B) Maximum is 14 for $x_{1}=4, x_{2}=1$
C) Maximum is 15 for $x_{1}=5, x_{2}=0$
D) Maximum is 13 for $x_{1}=3, x_{2}=2$