Find the minimum value of `Z=x+3y` in the constraints `x+y le 8`, `3x+5y ge 15`, `x ge 0`, `y ge 0`

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= 4x+5y subject to the constraints x le 30, yle 40 and x ge 0,y ge 0 is

Find the minimum value of Z=3x+5y, subject to the constraints -2x+y le4, x+y ge3, x-2yle2, x ge0 and y ge0.

The maximum value of Z = 3x + 5y subjected to the constraints x + y le 2, 4x + 3y le 12, x ge 0, y ge 0 is

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

Find the maximum value of x+y subjected to the condition 4x+3y le 12, 2x + 5y le 10, x le 0, x ge 0, y ge 0 .