`3x + 3y ge 24 , 3x + 4y le 15 , x ge 0 , y ge 0 `

Solve the following graphically x + 4y le 8 , 3x - 4y le 12 , x ge 0 , y ge 0

x +2y le 3, 3x + 4y ge 12 , x ge 0, y ge 1

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

Z =13x + 3y x + y le 6, 3x + 2y le 15, x ge 0, y ge 0 .

Draw the diagram of the solution set of 3x + 4y le 24, -3x + 2y le 6, x ge 0, y ge 0 .

Minimize (16-21): OBJECTIVE FUNCTION CONSTRAINTS Z = 200x + 500y x + 2y ge 10, 3x + 4y le 24, x ge 0, y ge 0 .

x + 2y le 3, 3x + 4y ge 12, x ge 0, y ge 1

Maximize z = 4 x + 5y , subject to 2x + y ge7, 2x + 3 y le 15, x le 3, x ge 0 , y ge 0

Maximize z =2x + 3y subject to constraints x + 4y le 8, 3x + 2y le 14 , x ge 0, y ge 0 .