Help! algebra 2 linear programming

I'm having trouble solving a linear programming question...

Q:
find the maximum for P = 2x + 3y when
x + 2y ≲ 24
3x + 2y ≲ 34
3x + y ≲ 29
x ≳ 0


I keep coming up with values that have decimal points
and i'm not sure if that's supposed to be correct :S

Help!

Also, could you please specify the values of x and y at its maximum?
Thank you.

The answer is
x = 5.0
y = 9.5
P = 38.5

I solved it with the simplex algorithm but i think you have learned to solve it graphically.
Draw the straight lines
x+2y-24 = 0
3x+2y-34=0
3x+y-29=0
And colour the area on the side of this line corresponding to the inequalities.
As (0,0) satisifies all three inequalities, this is on the side where the origin lies.
Colour the intersection of all 3 found area's in another colour.
Look at the corner points of this last area and calculate P for all corner points.
The corner with the biggest value for P is the answer !

Plot these linear inequalities to determine the Feasible region
Find the corner points ; if there is an unique solution it will be at one of these points

Evaluate P= 2x + 3y at each of the corner points, hopefully just one will give you a maximum value

(If two corner points give the same max value, then all points on the line segment between them also gives a maximum)