# 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.