Maximize

Z = f(x,y) = 5x + 3y

subject to:

x + 2y 20

2x + 3y 36

x + 3y 30

2y > 4

x > 0 , y > 0

So maximum will occur at one of the above 4 extreme points.

f (0,10)=30

f (0,2)=6

f (15,2)=81

f (12,4)=72

Hence the maximum value of f is 81 obtained at x=15 y y=2

All the intersection points are obtained by solving each pair of equations. Solution space is the shaded region with extreme points (0, 2), (0, 10), (15, 2), (12, 4). So maximum will occur at one of the above 4 extreme points. f(0, 10)=30 f(0, 10)=30 f(0, 2)=6 f(15, 2)=81 f(12, 4)=72 Hence the maximum value of f is 81 obtained of x=15, y=2 All the intersection points are obtained by solving each pair of equations. Solution space is the shaded region with extreme points (0, 2), (0, 10), (15, 2), (12, 4). So maximum will occur at one of the above 4 extreme points. f(0, 10)=30 f(0, 10)=30 f(0, 2)=6 f(15, 2)=81 f(12, 4)=72 Hence the maximum value of f is 81 obtained of x=15, y=2