`2x + y ge 6, x + 2y ge 8, x ge 0, y ge 0`

2x + y le 6, x + 2y le 8, x ge 0, y ge 0

2x + y le 6, x + 2y le 8, x ge 0, y ge 0

Z = 5x + 10y x + 2y le 120, x + y ge 60, x - 2y ge 0, x ge 0 , y ge 0 .

Minimize Z = 2x + 3y subject to constraints x + y ge 6 , 2x + y ge 7, x + 4y ge 8 , x ge 0 , y ge 0

Maximum Z = 3x + 5y subject to the constraints : x + 2y ge 10, x + y ge 6, 3x + y ge 8, x ge 0, y ge 0 .

x + y ge 24, 2x + y ge 32, x ge 0, y ge 0

Minimum of Z = x+ y subject to : 2x + y ge 3, x + 2y ge 6, x ge 0, y ge 0 is .........at ............

Minimize z = 24x + 40y subject to constraints 6x + 8y ge 96, 7x + 12y ge 168, x ge 0 , y ge 0

Graphically maximize Z = 6x + 9y subject to the constraints 2x - y ge 0, 2x + y ge 8, x + 11 y le 80, x ge 0, y ge 0 .