Good morning, I need some help or hints on finding the most "restrictive" equation in a set of equations and inequalities. I have a set of 30 single equations/inequalities in my set, namely:
eqs={y + 0.135456 z >= 78.4807, z >= 51.5464, x + 0.495376 y >= 79.1498,
x + 371.686 y >= 34406.8, x + 3.68043 y >= 243.273,
x + 0.523148 y + 2.1009 z >= 84.8248, x + 0.532835 y >= 66.3424,
x + 0.542384 y >= 75.3277, y + 1.65913 z >= 87.2085,
x >= 38.7097, y >= 75.6909, z >= 57.7224, z <= 51.5544,
y + 0.135456 z <= 98.1008, z <= 64.4124, y <= 6.25*10^7,
x + 2.42904 y + 2.18814 z <= 7260.06, y <= 3.57143*10^7,
x + 0.495376 y <= 131.905, x + 371.686 y <= 57372.9,
x + 3.68043 y <= 405.455, x + 0.523148 y + 2.1009 z <= 141.417,
x + 0.532835 y <= 110.488, x + 0.542384 y <= 125.465,
x <= 6.66667*10^7, y <= 166667., y + 1.65913 z <= 109.007,
x <= 47.3118, y <= 92.5111, z <= 70.5496}
Finally, I need to solve the whole set. If you apply FullSimplify[And@@eqs], you get False, which is correct; the 12th equation z >= 57.7224 and the 13th equation z <= 51.5544 are conflicting.
Instead of checking all combinations, I would like to have a "smarter" (and faster) way to find conflicting equations which restricts the whole system the most.
I was thinking of adding on equation after another, but this also involves a lot of combinations.
Do you have any ideas or hints? Thank you!
