[" Find the minimum value of "Z=2x+4y],[" subject to constraints "4x+3y<=12" ,"],[x+2y>=4,x,y>=0]

Find the minimum value of Z = -3x + 4y, subject to the constraints x+2y le 8, 3x+2y le 12, x ge 0, y ge 0 .

Find the minimum value of Z = x + y subject to the constraints 2x+3y le 6, 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.

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

Find the maximum value of Z = 4x + y subject to the constraints 2x+y le 23, x ge 0, y ge 0 is ……….

The minimum value of Z = 5x - 4y subject to constraints x+y le 10 , y le 4, x,y gt 0 will be at the point

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