The current feasible region.
Note the time constraint is the blue diagonal line.
The current constraint is 4x+6y<=480
Changing the time worked changes the 480, specifically increasing the time worked increases the 480, this in turn
will lift the blue line up.
Here I have plotted
4x+6y<=520
Note this line has moved up
from before.
You can see that once this line moves up far enough (like now) it has no effect on the feasible region. The last point
of the region defined by the other constraints that it will pass through is (60,45) ,
Note that (60,45) gives more profit so is now the new maximal point.
and the time equation needed is the line is 4x+6y (use (60,45))=510
And the answer follows