Question 1207825
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use graphical methods and the corner point theorem to maximize z=x+5y subject to 3x+2y<12
2x+y<7
x>0
y<0
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With the inequality signs written/presented in your post, &nbsp;function &nbsp;&nbsp;z = x + 5y &nbsp;&nbsp;has no maximum 
in the feasibility domain.


So, &nbsp;the problem, &nbsp;as formulated in the post, &nbsp;does not have a solution, &nbsp;at all.



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&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;The corner points theorem is inapplicable in this case, &nbsp;since the corner points,

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;defined by inequalities in your post, do not belong to the feasibility domain.


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In order for the problem be meaningful and would have a solution, &nbsp;the problem should be &nbsp;RE-formulated 
and the inequality signs should be changed.



So, &nbsp;guided by these my notices, &nbsp;double check your post, &nbsp;comparing it with the source.



If the problem, &nbsp;as written in your post, &nbsp;coincide with the source, &nbsp;then the problem is a &nbsp;TRAP &nbsp;and has no solution.


In case, &nbsp;if you detect errors in your post, &nbsp;fix them and re-post the fixed version to the forum.


If you do it, then please do not post the problem to me in person - re-post as you usually post to this forum,
through the central gate.



As the lesson to learn for the future, &nbsp;memorize that &nbsp;Math does not tolerate inaccuracy.