Hi, I have the following question and I need to know if i have augmented it correctly and what my next steps should be.

$\displaystyle Z = x_{1} + 4x_{2}$

Maximise

subject to

$\displaystyle -3x_{1} + x_{2} \leq 6$

$\displaystyle x_{1} + 2x_{2} \leq 4$

and$\displaystyle x_{2} \geq -3$

My steps to solve were

let $\displaystyle x'_{2} = x_{2} + 3$

so then we have:

$\displaystyle Z = x_{1} + 4x'_{2} -12$

$\displaystyle -3x_{1} + x'_{2} \leq 9$

$\displaystyle x_{1} + 2x'_{2} \leq 10$

and$\displaystyle x'_{2} \geq 0$

i thought this was the correct augmented form of the LPP, however, none of the multiple choice answers i can choose from show this, hence i know it is wrong, but I'm not sure what i have done wrong, all the answers have added more variables.