Solve the following linear programming problem graphically :
Minimize `Z=x+2y`
subject to `2x+y ge 3, x+2y ge 6,x,y ge 0`.

Minimise Z=x+2y subject to 2x+y ge 3,x+2y ge 6, x, y ge 0

(i) Draw the graph of lines x+y=8,3x+5y=15 (ii) Solve the following linear programming problem graphically Minimise Z=3x+2y Subject to constraints x+y ge 8 3x+5y le 15 x,y ge 0

2x+y ge 6

Solve the following linear programming problem graphically. Minimize Z=200 x+500 y subject to the constraints: x+2y ge10 3x+4y le 24 x ge0, y, ge0

2x+y ge 8, x+2y ge 10

Minimize Z=3x+5y such that x+3y ge 3, x +y ge 2, x, y ge 0 .

Solve the following linear programming problem graphically: Maximise Z=4x+y ………….1 subject to the constraints: x+yle50 ……………2 3x+yle90 …………..3 xge0, yge0 …………..4

x ge 3, y ge 2

-3x + 2y ge -6