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I understood that the range for x0 will be from [0,4] which is maximum of the upperbound and minimum of the lower bound. 

I believe that, i can choose any values from [0,4] when i select x0 =4 , I got the last inequalities, that's also fine. But how can we conclude that  x1= 4 as the solution when we select x0=4? (Here there is an inequality 4<=x1<=4 , is it because of that? 

What will have happen instead of 4<=x1<=4 , if we have  4<=x1<=5, then what  is the value of x1? Can we select any value? )

Could you please help on this?

 

in # Study-Organisation (Master) by (2.7k points)
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Yes, you can select any value in the determined interval. For the last variable that is left, we have already such an interval determined by the greatest of the lower bounds and the least of the upper bounds.

Once determined such a value, you get another interval in the same way for the next variable, and so on. In particular, you can thereby select integer values if there is an integer solution which makes Fourier-Motzkin not more difficult for integers than for reals. Even more, you can also handle inequalities with < instead of <= which is not possible with Simplex.
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Thank you professor for the clarification. I understood.

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