Thread: Linear Programing - Negative Numbers Help

Hi,

I have a question about what to do with a constraint that is negative.

A: -3x1 + x2 = 90

So I get x1= -30, and x2 = 90.

I have a feeling this isn't right since linear models should not have negative numbers.

Can anyone help me out?

Originally Posted by guthrie23

Hi,

I have a question about what to do with a constraint that is negative.

A: -3x1 + x2 = 90

So I get x1= -30, and x2 = 90.

I have a feeling this isn't right since linear models should not have negative numbers.

Can anyone help me out?

Could you post the whole question? If we can see the problem in its entirety, we may be able to assist you more since there are methods that help us deal with LP problems that have "negative" constraits (methods like the Dual-Simplex method).

Constraint A: -3X1 + X2 =< 90
Constraint B: 4X1 - 2X2 >= 120
Constraint C: X1 + 2X2 =< 150
All variables are required to be non-negative. Let the objective function be Min: 2X1 - 3X2. What are the corner points of feasible solution region?

X1 = 54, x2 = 48 : 2x1 - 3x2 = -36

Originally Posted by guthrie23

Constraint A: -3X1 + X2 =< 90
Constraint B: 4X1 - 2X2 >= 120
Constraint C: X1 + 2X2 =< 150
All variables are required to be non-negative. Let the objective function be Min: 2X1 - 3X2. What are the corner points of feasible solution region?

Rewrite the constraints:

x_2 <= 90 + 3 x_1

x_2 <= -60 + 2 x_1

x_2 <= 75 - x_1/2

x_1 >=0, x_2>=0

Plot these constraints and the vertices of the feasible region will be obvious.

CB

Wilmer, How did you get those answers?

Loopy-de-loop program; a bit like:

Loop X1, X2
If -3*X1 + X2 > 90
or 4*X1 - 2*X2 < 120
or X1 + 2*X2 > 150
then get out of here, else
M = 2*X1 - 3*X2
Store M if lower than last M

Originally Posted by guthrie23

Wilmer, How did you get those answers?

You will note that Wilmer's post does not answer the question you posted.

CB