The minimum value of f=x+4y subject to the constraints `x+y ge 8, 2x+y ge 10,x gt 0, y gt 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

The minimum value of Z = 4x + 5y subjected to the constraints x + y ge 6, 5x + y ge 10 , x ge 0, y ge 0 is

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 minimum value of z = 2x + 4y subject to constraints x+2y ge 10, 3x+y ge 10, x ge 0, y ge 0 is ………..

The minimum value of Z= 4x+5y subject to the constraints x le 30, yle 40 and x ge 0,y ge 0 is

The minimum value of 2x + 3y subject to the condition x+4y ge 8, 4x+y ge 12, x ge 0 and 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 ………

Maximum value of Z = 3x + 4y subject to the constraints x + y le 4, x ge 0, y ge 0 is 16.