# Solving a system of inequalities

I'm trying to solve a system of inequalities with $6$ variables using Reduce but it's taking a long time (at least 30 mins) and has not yet finished.

Reduce[{2 b + d <= 2 c + h, 2 e <= 2 b + a, e + b + d <= 2 c + h,
2 e + d <= a + h + 2 c,
2 e + 2 b + 2 d <= 4 c + 2 h, (150/100) (2 b + 2 c) <
2 e + 2 b + 2 d, (150/100) (e + d + h + c) <
2 e + 2 b + 2 d, (150/100) (d + a + h) < 2 e + 2 b + 2 d, b > 0,
c > 0, d > 0, e > 0 , h > 0, a > 0}, {a, b, c, d, e, h}]


Any recommendations on making this run faster (or at least have it finish)? I recently started using Mathematica so I'm not familiar with any of the methods for making computation run faster.

• Maple says there is no solution. – user64494 Mar 1 '18 at 20:09

## 1 Answer

There is no solution of the system under consideration. Even

Reduce[{2 b + d <= 2 c + h, 2 e <= 2 b + a, e + b + d <= 2 c + h,
2 e + d <= a + h + 2 c, 2 e + 2 b + 2 d <= 4 c + 2 h, (150/100) (2 b + 2 c) <
2 e + 2 b + 2 d, (150/100) (e + d + h + c) < 2 e + 2 b + 2 d, (150/100) (d + a + h) <
2 e + 2 b + 2 d, b > 0, c > 0, d > 0, e > 0, h > 0, a > 0}, {a}, Reals]//AbsoluteTiming


{7.23154, False}