problem has no solution using graphical method 2 If the maximum value of z appears only at o then the problem has unbounded solution 3 If the maximum value of z appears at 2 points there exists infinite number of solutions to the LPP Problem 4 Find the maximum value of z to the following LPP using graphical method Max z 5x 7x2 subject to x x2 4 3x1 8x2 24 10x 7x 35 and x 0 Vi 1 2 Solution The given problem contains only two variables x and x So graphical method is possible Consider the equations we get X X 4 3x 8x 24 Now to find the points Consider x x 4 Put x 0 x 4 10x 7x 35 and x 0 x 4 Therefore 0 4 and 4 0 are the pts Similarly consider 3x 8x 24 We get 0 3 and 8 0 are the pts Consider 10x 7x 35 We get 0 5 and 3 5 0 are the pts The graphical representation is