ok, lets hope you can help me out!
and must lie within or on the boundary of shaded region of my drawing
* What are the two constraints on the problem?
* Whats the max. value of the within the shaded region?
If this line has to pass at least through one point of the shaded region. f gets a maximum if the line is translated as much up as possible.
Thus f is maximal if x = 0 and y = 6. In this case f = 36.
Have a look at the graph which I posted with my previous reply:
.... and .....
Since the line has to pass through the highest point of the region build by the constraints, so that the value of f becomes a maximum, you have to look for this "highest" point. You find it in the first part of the constraints.