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_12x_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