[MOVED] Linear Programming: find corner pts, evaluate

[chizik10]

Find the coordinates of the corner points.

2(x1) - 3(x2) >= -8
2(x1) + 6(x2) >= 28
4(x1) + 3(x2) <= 38
x1, x2 >= 0

The objective function is P= 2(x1) + 12(x2). Evaluate it at all the corner points, and find the maximum and minimum.

I'm so confused i'm using Maple TA and it has shown me a feasible region that is supposed to be similar to these inequalities but I don't know how to use my graphing calculator to get the points.

I believe I am making this harder than it should be

 

[Deleted member 4993]

Re: Linear Programming

2(x1) - 3(x2)>= -8
2(x1) + 6(x2) >= 28
4(x1) + 3(x2)<= 38
x1, x2>=0

Instead of (x1,x2) use (x,y) - all those are straight lines - should not be problematic in graphing calculator (heck, you shouldn't even use calculator for this problem - just sketch it by hand).

 

[stapel]

Find the coordinates of the corner points.

2(x1) - 3(x2) >= -8
2(x1) + 6(x2) >= 28
4(x1) + 3(x2) <= 38
x1, x2 >= 0

The previous reply is an excellent one! To graph, convert to more-familiar coordinates:

. . . . .2x - 3y > -8

. . . . .2x + 6y > 28

. . . . .4x + 3y < 38

. . . . .x, y >

To graph, it's generally helpful to solve to get "y" by itself. For instance, the first inequality would become:

. . . . .2x - 3y > -8

. . . . .2x + 8 > 3y

. . . . .(2/3)x + (8/3) > y

. . . . .y < (2/3)x + (8/3)

Graph the line "y = (2/3)x + (8/3)", and then, since you want "y less than", shade below the line.

To find the corner points, set pairs of lines equal to each other, and solve for the intersection x-values. Back-solve for the intersection y-values. For instance, the first two lines intersect at:

. . . . .(2/3)x + (8/3) = -(1/3)x + (14/3)

. . . . .2x + 8 = -x + 14

. . . . .3x + 8 = 14

. . . . .3x = 6

. . . . .x = 2

Then y = 4, and (x, y) = (2, 4) is a corner point.

Once you find all the corner points, including where the horizontal line y = 0 and the vertical line x = 0 cross the other lines, you plug those into the objective function, and find the points which give the highest value and lowest value of P.

For a lesson with worked examples, try here.

Have fun!

Eliz.