I am currently trying to solve a system of equations with numerous constraints by using the simplex linear programming method. I have 6 variables (x1 to x6) and 22 total constraints. The constraints are base on 11 variables (y1 to y11) that are dependent on x1 through x6. Each of the y has a lower and an upper bound which create 2 inequality constraints.

upper:

y1 = a1x1 + a2x2 + ... + a(n)x(n) <= A

lower:

y1 = a1x1 + a2x2 + ... + a(n)x(n) >= B

My objective is to maximize E = c1x1 + c2x2 + ... + c(n)xn

where c can be negative constants.

To fully understand this problem, I start with just the first 2 constraints for y1 and ran the simplex algorithm that I wrote. The solution satisfy the bounds for y1.

I then add the constraints for y2 and run the problem with 4 total constraints. Again, the result satisfy the bounds for y1, and y2.

The process is repeated until I reach y7. The simplex method found an answer; however, one of my previous constraints is no longer satisfy. I tried running this same problem in the Excel Simplex LP Solver and the results satisfy all of my constraints (y1 to y7).

Without going into the details of the problem, does any of you have experience in troubleshooting this issue? There is obviously a correct answer since excel simplex solver is able to get it. I am trying to understand why I am having trouble getting my simplex model to do so.

Thank you,