Old Linear programming  up where it may be found
posted by Damon .
Posted by Anonymous on Wednesday, November 26, 2008 at 8:49pm.
P=30x+25y
Subject to 2x+3y>=30
2x+y<=26
6x+5y<=50
x,y>=0
I need the minimize and maximaze
Responses
* linear programming problem  Damon, Thursday, November 27, 2008 at 1:35pm
One point at the origin, constrained to first quadrant.
first constraint #1
2x+3y>=30
when x = 0, y = 10
when x = 15, y = 0
area above that line is in our region (are you sure your arrow is correct?)
second constraint #2
2x+y<=26
when x = 0, y = 26
when x = 13, y = 0
area below that line is in
third constraint #3
6x+5y<=50
when x = 0, y = 10
when x = 50/6 or 8 1/3 , y = 0
area below that line is in
sketch a graph. You see that our region of interest is a triangle from (0,10) to the intersection of #2 and #3 down to the intersection of #1 and #2
first #1 and #2
2x+3y=30
2x+y=26
gives
2 y = 4 or y = 2 then x = 12
so (12,2)
now #2 and #3
2x + y=26 >6 x + 3y = 78
6x+5y=50
gives
8y = 128
y = 16 then x = 5
so (5,16)
NOW
calculate P at (5,16) and (12,2) and (0,10) and chose the biggest or smallest whichever you want. If P is "profit", you probably want the biggest.
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