Maximise Z = 2X1 + X2
subject to:
X1 + 3X2 <= 25
3X1 + 3X2 = 15
2X1 + X2 >= 4
X1, X2 >= 0
You can solve this by gaphical method, i.e.
1. You plot the constraints,taking x1 as x and x2 as y, {feasible region)
2. plot the objective fcn using two different values of z, (iso-lines)
3. observe the direction of 2. as z increases
4. Find out the last point(may also be a segment) in the feasible region which will be touched by an iso line.
if you do this, you'll notice that you're feasible region is a line (the second constraint). The last point of that line that will be touched by the iso lines (iso-lines are actually parallel to the third constraint and it is actually heading towards the direction of the origin) is the point (0,5). This gives you the maximum z=5.
You can also use simplex method but that entails more time and effort. Since your problem involves only two variables, it's much easier to graph.