Maximize Z = 3x + 4y , subject to the constraints are ` x + y le 4, x ge 0 " and " y ge 0 `.

Maximize Z = 3x + 5y, subject to constraints are x + 3y le 3, x + y le 2 " and " x ,y ge 0 .

Maximize Z = x + y, subject to constraints are x - y le - 1, - x + y le 0 " and " x, y ge 0 .

Maximize Z = 3x + 2y, subject to constraints are x + 2y le 10, 3x + y le 15, " and " x , y ge 0 .

Minimize Z= x + 2y, subject to constraints are 2x + y ge 3, x + 2y ge 6 , " and " x , y ge 0 . Show that the minimum of Z occurs at more than two point .

For the LPP, maximize z = x + 4y subject to the constraints x + 2y le 2, x +2y ge 8, x, y ge 0 .

Maximize and Minimize Z = 5x + 10y , subject to constraints are x + 2y le 120 , x + y ge 60, x - 2y ge 0 " and " x, y ge 0 .

Maximize Z = 5x + 3y, subject to constraints are 3x + 5y le 15 , 5x + 2y le 10 , x ge 0 " and " y ge 0 .

Minimise and Maximise Z = x + 2y, subject to constraints are x + 2y ge 100, 2x - y le 0, 2x + y le 200 " and " x,y ge 0 .

Minimize Z = - x + 2y, subject to constraints are x ge3, x + y ge 5 , x + 2y ge 6 " and " x , y ge 0 .

(a)Maximise z = 4x + y subject to constraints : x + y le 50 3x + y le 90 x ge 0 y ge 0 by graphical method. (b) Find the value of K, if f(x) = {{:(Kx + 1, "if"x le pi),(cos x, "if " x gt pi):} is continuous at x = pi .