#unknown in LP maximisation problem

19 messages · Page 1 of 1 (latest)

civic salmon
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In this LP maximisation problem the equation we have to maximise has an unknown in it that does not appear in the constraints. Furthermore the question asks to find all p such that there are infinitely many solutions. What does the p entail? Are we supposed to find a p that makes it so that the critical points of the feasibility region put into the objective function have the same value? Is there a reason we cannot just say p > k for concrete k as that would make infinitely many optimal solutions for a given set of points?

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echo geodeBOT
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frozen mauve
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Your suggestion would be: get some k and prove that for p > k, Problem(p) has infinite optimal solutions, right?

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But that would get you a subset of what the question asks you

civic salmon
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Something along those lines

frozen mauve
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Well, that would get you Solution inter ]k: infinity[

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Not solution

civic salmon
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To me it seems that p could be anything as long as we have values for x, y, since then we should have an optimal solution, that's what I do not understand about the question

frozen mauve
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The question is that you have a set of many problems that depend on a parameter p

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Problems = {Problem(p) for p in R}

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And you want to find which of them have infinite optimal solutions

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So naturally you inspect Problem(p) for each p

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And see if it is the case that you have infinite optimal solutions or not

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And the question asks you for all the p where it is the case

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It has nothing to do with determined values of x and y

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I mean it does in a way but that's not what the question is about

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Does that make sense?