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Linear optimization problem

I currently have the following scenario and i am having some trouble creating a linear program to model the problem.

Currently i have the linear model as such, however i believe that this does not fully model the problem.

Maximize $w_1 + w_2 + w_3$

Subject To

R1: $40 x_1 + 40 x_2 + w_1 + w_2 + w_3 + 30 \geq 0$

R2: $40 x_3 + 40 x_4 + w_2 + w_3 + 20 \geq 0$

R3: $40 x_5 + 40 x_6 + w_3 + 10 \geq 0$

R4: $x_1 + x_2 + x_3 + x_4 + x_5 + 2 x_6 \leq 60$

R5: $w_3 + w_2 - w_1 \leq 0$

R6: $w_1 + w_2 - w_3 \leq 0$

I have had it like this for a few days now and am starting to lose hope in figuring it out, any assistance would be much appreciated. I'm not from a maths background, so please be constructive.

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  • $\begingroup$ Welcome to math.SE. Please see math.meta.stackexchange.com/questions/588/… for information on how to attract quality answers. Proper formatting is expected; for information about writing math at this site see e.g. here, here, here and here. $\endgroup$ – mlc Oct 19 '17 at 17:58
  • $\begingroup$ Crossposted and answered at stackoverflow.com/questions/46833270/… $\endgroup$ – Erwin Kalvelagen Oct 19 '17 at 18:55
  • $\begingroup$ Not answered in any way remotely helpful ... and told it didn’t belong there, so posted in a maths specific place. So please don’t dismiss my question when I’m seeking help. $\endgroup$ – user7816680 Oct 19 '17 at 18:58
  • $\begingroup$ For R1-R3, you have "load weight (in terms of w) $\le$ weight capacity (in terms of x)", so $x$ and $w$ should have opposite signs. R4 is correct. R5&R6 should be written the opposite way: $w_1\le w_2+w_3$, etc, as stated in the question "$w_1$ ... does not exceed ... $w_2+w_3$". $\endgroup$ – GNUSupporter 8964民主女神 地下教會 Dec 21 '17 at 17:08

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