Minimize `z=6x+3y` subject to the constraints `4x+y ge 80 , x +5y gt 115, 3x+2y le 150 , 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

Minimize Z = 3x + 2y subject to the constraints : x + y ge 8, 3x + 5y le 15, x ge 0, y ge 0 .

Solve the LPP graphically: Minimize Z = 4x + 5y Subject to the constraints 5x + y ge 10, x + y ge 6, x + 4y ge 12, x , y ge 0

Maximize Z = 5x + 3y subject to the constraints: 3x + 5y le 15, 5x + 2y le 10, 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 .

The linear programming problem minimiseZ=3x+2y subject to the constraints x+y ge 8 3x +5y le 15 x ge 0, y ge 0 has

Minimize 3x+2y subject to the constraints x+y ge 5 and x+2 y ge 6, x ge0, y ge 0

Maximise and Minimise : Z = 4x + 3y -7 subject to the constraints: x + y le 10, x + y ge 3, x le 8, y le 9, x, y ge 0

Maximize: Z = -x + 2y , subject to the constraints: x ge 3, x + y ge 5, x + 2y ge 6, y ge 0 .

Maximise Z= -x + 2y , subject to the constraints: x ge 3, x + y ge 5, x + 2y ge 6, y ge 0 .