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How to find most negative number amongst (2M-1), (-2M+7), (-3M+10) and (-M+3). If we put M = 1 we get all positive answers. But we need most negative number.

Please tell me what more information should i give? or how to reformat question? what details i should give?

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closed as not a real question by Jonas Meyer, Andres Caicedo, Rasmus, t.b., Fabian Jun 12 '11 at 19:40

It's difficult to tell what is being asked here. This question is ambiguous, vague, incomplete, overly broad, or rhetorical and cannot be reasonably answered in its current form. For help clarifying this question so that it can be reopened, visit the help center.If this question can be reworded to fit the rules in the help center, please edit the question.

    
@Abhijit: What exactly are u looking for. Do you need all the $(2M-1), (-2M+7)$ $\cdots$ to be negative –  user9413 Jun 12 '11 at 5:33
    
ammm no. i dont 'need' all them to be negative. i am looking for which one of them is 'most negative' –  Abhijit Navale Jun 12 '11 at 5:34
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As far as I know there is nothing called as most negative. May be you are missing something –  user9413 Jun 12 '11 at 5:40
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-1 The question, as stated, is unclear and somewhat confusing. I do not understand why this was voted up. The proper mathematical term for "most negative" is "smallest". Therefore, you wish to find the smallest number. However, it is not clear what numbers you are considering. You write: "If we put $M=1$ we get all positive answers. But we need most negative number." What exactly would you like us to do? Do you want to find the smallest number among these when $M=1$? Or do you want to find the smallest number among these for general $M$? How do we know what details you should give? –  Amitesh Datta Jun 12 '11 at 5:50
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@Abhijit As stated, this question seems to have a straightforward answer that doesn't require "Dual LPP". If this isn't what you're looking for, could you perhaps provide more context? –  Elliott Jun 12 '11 at 9:14

1 Answer 1

I assume you want to find $\min(2M-1,-2M+7,-3M+10,-M+3)$ as a function of $M$. The answer is $2M-1$ if $M \le 4/3$, $-M+3$ if $4/3 \le M \le 7/2$, and $-3M+10$ if $M \ge 7/2$.

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Robert no offense just asking to make sure but do you know how to solve Dual LPP? –  Abhijit Navale Jun 12 '11 at 6:08
    
@Abhijit: Since there is only one variable here, there is no need to "solve Dual LPP", it can be solved directly. –  Yuval Filmus Jun 12 '11 at 6:43

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