The maximum value of Z = 4x + 2y subject to the constraints `2x+3y le 18,x+y ge 10, x , y ge 0 ` is

The maximum value of Z = 4x + 2y subjected to the constraints 2x + 3y le 18, x + y ge 10, where x, y ge 0 is :

The maximum value of Z = x + 3y subject to the constraints 2x+y le 20, x+2y le 20, x ge 0, y ge 0 is ……….

The maximum value of Z = x + 4y subject to the constraints 3x+6y le 6, 4x+8y ge 16, x ge 0, y ge 0 is ………

Find the maximum value of Z = x + y, subject to the constraints x-y le -1, -x+y le 0, x, y ge 0 .

The point at which the maximum value of Z = 3x + 2y subject to the constraints x+2y le 2, x ge 0, y ge 0 is ……….

The point at which the minimum value of z = 8x + 12y subject to the constraints 2x +y ge 8, x + 2y ge 10 x ge 0, y ge 0 is obtained is