Draw the graphs of X+2Y=8 and 5X+4Y=20. The corner point is where the lines cross, and this can be found by solving the two line equations as simultaneous equations. If we double eqn 1 and subtract from eqn 2 we get 3X=4 so X=4/3 and therefore, by substituting for X in either eqn we get Y=10/3. The area below the lines enclosed by the both lines and the X and Y axes, is the region in which all the given conditions are met. The maximum profit occurs at the corner point, so max profit=4X+6Y=16/3+20=76/3=25.33.