# Thread: Linear Programming Problem HELP NEEDED

1. ## Linear Programming Problem HELP NEEDED

Please show that the following linear program is infeasible:

maximize
3x1
-
2x2
subject to
x1
+
x2

2
-2x1
-
2x2

-10
x1, x2

0 .

2. Originally Posted by tcpipmen
Please show that the following linear program is infeasible:

maximize
3x1
-
2x2
subject to
x1
+
x2

2
-2x1
-
2x2

-10
x1, x2

0 .
First, do you really expect any help with this formated the way it is?

Look at your constaints, the first is:

x_1+x_2<=2

The second is:

-2x_1-2x_2<=-10

multiply this through by -1, which changes the direction of the inequality to give:

2x_1+2x_2>=10

Now divide though by 2 to get:

x_1+x_2>=5

So we have for a feasible point (x_1,x_2):

x_1+x_2<=2 and x_1+x_2>=5

which is a contradiction, so there are no feasible points, and so the problem is infeasible.

RonL

thanks