# Thread: Linear Programing Problem, Simplex but with a negative constraint?

1. ## [SOLVED] Linear Programing Problem, Simplex but with a negative constraint?

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

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

2. ## Re: Linear Programing Problem, Simplex but with a negative constraint?

I have come up with this as my augmented problem:

$\displaystyle Z = x^+_{1} - x^-_{1} + 4x'_{2} -12$
$\displaystyle -3x^+_{1} + 3x^-_{1} + x'_{2} + x_{3} = 9$
$\displaystyle x^+_{1} - x^-_{1} + 2x'_{2} + x_{4} = 10$
$\displaystyle x^+_{1} \geq 0, x^-_{1} \geq 0, x'_{2} \geq 0, x_{3} \geq 0, x_{4} \geq 0$

However, when i try to solve this in a tableau i don't get any of the answers given.
Am i first supposed to change the first equation so that $\displaystyle x^+_{1}, x^-_{1}$ and $\displaystyle x'_{2}$ coefficients are to equal zero or just some of the variables.

Solved