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 $w_1 + w_2 + w_3$
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.