Use the Two-Stage Method to Solve $w=5 x_{1}+2 x_{2}$ Subject To $x_{1}+x_{2}=10$

Multiple Choice

Use the two-stage method to solve.
-Minimize $w=5 x_{1}+2 x_{2}$
Subject to: $x_{1}+x_{2}=10$
$3 x_{1}+x_{2} \geq 18$
$\mathrm{x}_{1}+2 \mathrm{x}_{2} \leq 12$
$x_{1} \geq 0, x_{2} \geq 0$

A) Minimum is 41 for $x_{1}=7, x_{2}=3$
B) Minimum is 44 for $x_{1}=8, x_{2}=2$
C) Minimum is 20 for $x_{1}=0, x_{2}=10$
D) Minimum is 32 for $x_{1}=4, x_{2}=6$