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I'm working on what I think is a fairly basic LP problem, the objective function and constraints are seen in the attached image. The task also specifies that the starting basis should be x1, x2, x3, x5, x6 where the slack variables are x3 through x7. However, as soon as I get to working on it with the tables, I run into the issue that the most negative coefficient is the -10 which is associated with x1. From what I learned, that variable is supposed to enter the basis, but in this case x1 is already in the basis to begin with. What do I do in that case? Just got started with LP so probably missing something simple.

Thanks! Problem

Peter Robertsson
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  • Have you introduced artificial variables? – callculus42 Nov 15 '23 at 18:19
  • I have not, we just learned about them today. I guess I must've misunderstood them a bit. The way I understood it is that we introduce them when we cannot identify any basic variables. I thought that since the task specified a basis (x1, x2, x3, x5, x6) that wouldn't be necessary. Should I be adding artifical variables to the first and second constraint then? – Peter Robertsson Nov 15 '23 at 18:40
  • That is completely right. Here are two expamples how to start: 1 and 2 – callculus42 Nov 15 '23 at 18:57
  • I've been able to solve it now, but I feel like I'm completely ignoring the part where the problem explicitly says that x1, x2, x3, x5 and x6 should form the initial basis. Perhaps I'm just misunderstanding it, but how could e.g x1 be a basic variable? I thought basic variables had to have unit columns, which x1 definitely won't have unless I've made a big error. – Peter Robertsson Nov 15 '23 at 23:54

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