Minimize `z = 2x + 3y`, such that `1 le x + 2y le 10, x ge 0, y ge 0`.

Maximum z = 30x + 19y such that x + y le24, x+1/2y le 16, x ge 0, y ge 0 .

Minimise Z = –x + y subject to: x – y le –1, –x + y le 0, x, y ge 0

Maximise Z = –x + y subject to: x – y le –1, –x + y le 0, x, y ge 0

Solve the following linear programming problems graphically Maximise Z = 3x + 2y subject to x + 2y le 10 , 3x + y le 15 , x,y ge 0