Reucing / solving inequality

Questions
,
1

How can I reduce following inequalities in mathematica:

x1 ? 2 , x2 ? 1, x3 ? 2, x1 + x2 ? 4, x1 + x3 ? 7, x2 + x3 ? 10

And
x1 + x2 + x3 = 14

I reduce and get:
2 ? x1 ? 4,
1 ? x2 ? 7,
2?x3 ?10,
x1+x2 + x3 = 14.
This is the result I want, but I can’t find the right code in mathematica.

2

Just Reduce it!

In[151]:= Reduce[{x1 >= 2, x2 >= 1, x3 >= 2, x1 + x2 >= 4, 
  x1 + x3 >= 7, x2 + x3 >= 10, x1 + x2 + x3 == 14}, {x1, x2, x3}]

Out[151]= ((2 <= x1 <= 3 && 4 - x1 <= x2 <= 7) || (3 < x1 <= 4 && 
     1 <= x2 <= 7)) && x3 == 14 - x1 - x2
3

With Mathematica, the commands are named for the operation they perform with a capitalized first letter. Therefore if for example you have the mathematical feeling that you should probably solve, reduce, integrate or whatnot, simply type that up in the documentation center and you will find the proper syntax. Have fun using Mathematica!