the objective function has a straight line as it's graph and the value for z correspond with the y-intercept of this line:
. That means: Take the y-intercept from the drawing and multiply it by 4 to get z.
These inequaltities will give a pentagon.
Now draw parallel lines through the vertices of the pentagon which have the slope . The greater the y-intercept the greater the value for z. If you use the point (10, 5) then the function with the greatest y-intercept is:
(1) I forgot to draw the line:
(2) the axes have different scales!