# Finding an assignment that satisfies a set of inequalities

I have the following simple set of inequalities:

var('x,y')
assume(x,'integer')
assume(y,'integer')
assume(x>0)
assume(y>0)
ineq = [x<y, y<3]


I would like to find an assignment that satisfies this set of inequalities. In this case there is one such assignment:

x=1, y=2


In general there may be many assignments; I only need to find one. Is there a way to do this in SageMath?

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Since your equations are linear, and your constraints about the variables is that they are integer, i strongly suggest to look at linear programming in Sage:

Do not hesitate to ask for more details if something is not clear (with your attempts so that we can discuss them).

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I read the manual about linear programming, but, apparently it talks about maximization problems. I am not interested in maximization - I only want to find a single assignment that satisfies the inequalities. Can you show me how to solve a simple example, e.g, "find x and y such that x<y and y<3"?