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July 18th, 2016, 03:00 AM   #1
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From: tehran

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how to selecte 2 inequalities between three inequalities for solving linear programmi

hi
i saw a question in a book for liner programming in solving the question i faced three inequalities as follow
1- 3x+2y<= 5000
2- 1x+.5y<= 1600
3- 4x+5y<= 9600
in book they select 1 and 3 inequalities for solving simultaneous equation, i cant understand the logic for this. anyone know the logic?
thanks in advances
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July 18th, 2016, 09:42 AM   #2
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Didn't you graph these? That should be the first thing you do with problems like this! First, those are "dashes" after the "1", "2", and "3" right? I first mistook them for minus signs!

To graph "3x+ 2y<= 5000", Graph the line "3x+ 2y= 5000" and, since, x= 0, y= 0 lies "to the left and below" that line, that is the set of points "to the left and below" that line. Similarly for the other inequalities.

Graphing (as I did in about three minutes), you should see that the two lines given by "x+ .5y= 1600"


Also, did you read the entire solution to the problem? They can't get the answer by finding only the intersection of the lines 1 and 3. They would also need to find the intersection of lines 2 and 3. The intersection of lines 1 and 2 are above the line 3 so not relevant.
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July 18th, 2016, 08:10 PM   #3
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From: tehran

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thanks dear country boy
as i understood, because this is a profit maximizing problem and so the optimal point is on intersection of line that is more far from the origin this mean " the intersection of line 1 and 3" and for finding the exact amount, equation 1 and 3 must be selected. the intersection of line 2 with other line is not a optimal point so must forgive this one.
thank you very much again.
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