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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.

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  • $\begingroup$ Maple says there is no solution. $\endgroup$ – user64494 Mar 1 '18 at 20:09
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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}

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