[" 9.Find the minimum value of "3x+5y" subject to "],[" constraints "-2x+y<=4,x+y>=3],[x-2y<=2,x,y>=0]

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 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 ……….

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

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

Find the minimum and maximum value of function Z=3x+4y subject to constraints are x>=0,y>=0,x+2y<=10 and 2x+y<=14