The coordinates of the point for minimum value of `Z=7x-8y` , subject to the conditions `x+y le 20 , y ge 5 ` and `x ge 0` are-

The coordinate of the point at which minimum value of Z = 7x - 8y, subject to the conditions constraints x+y - 20 le 0, y ge 5, le -5 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 minimum value of P = 6x + 16y subject to constraints x le 40 , y le 20 and x , y ge 0 is

Find maximum value of z=2x+3y subject to the constraints x+y le 4 , x ge 0 , y ge 0 .

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

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 + 4y, subject to the constraints x+2y le 8, 3x+2y le 12, x ge 0, y ge 0 .

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 .