`x + y ge 24, 2x+y ge 32, x ge 0, y ge 0`

The solution set of x - 2y ge 0, 2x - y le -2, x ge 0, y ge 0 is

Minimize Z = x + 4y subject to constraints x + 3y ge 3 , 2x + y ge 2, x ge 0 , y ge 0

Minimize z = 7x + y , subject to 5x + y ge 5, x + y ge 3, x ge 0 , y ge 0 .

(a) Draw the feasible region of inequation: x + y le 4, x ge 0, y ge 0 (b) Draw the graph of the following LPP: 3x + y le 17, x, y ge 0 (c) Shade the feasible region of LLP: (i) x + 3y ge 3, x + y ge 2, x ge 0, y ge 0 (ii) x + 2y le 8, 3x + 2y le 12, x ge 0, y ge 0

2x + y ge 6, x + 2y ge 8, x ge 0, y ge 0

2x + y ge 6, x + 2y ge 8, x ge 0, y ge 0

Z = 3x + 5y x + 3y ge 3, x + y ge 2,x ge 0, y ge 0

Z = 3x + 5y x + y ge 2, x + 3y ge 3 x ge 0 ,y ge 0