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minimize $max ${x1,x2}

subject to
$2x1+5x2<=9$
$x1+3x2<=5$
$x1>=0$, $x2>=0$

show that both are same and give reason

minimize t
subject to t>=x1 , t>=x2
$2x1+5x2<=9$
$x1+3x2<=5$
x1>=0, x2>=0

i tried
let t>=max{x1,x2}
then t>=x1 and t>=x2
am i right? but i dont understand the reason. please give me some hint thankyou

LarrySnyder610
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  • Please edit your question to typeset the math as actual math -- for example, use $2x_1 + 5x_2 \le 9$ instead of $2x1 + 5x2 <= 9$, and so on. There's a MathJax tutorial specifically related to linear programming here: https://math.meta.stackexchange.com/a/27756/663638 – LarrySnyder610 Apr 21 '19 at 23:18
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    As for your actual question: The general approach for showing that two LPs are equivalent is to show every feasible solution for one problem can be converted to a feasible solution for the other with the same objective function value. Can you make use of that approach? – LarrySnyder610 Apr 21 '19 at 23:22

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