Question
Solve the following linear programming problem graphically.
Maximize z = 11x + 5y
subject to the constraints
3x + 2y ≤ 25, x + y ≤ 10, x, y ≥ 0
Solution
We are to maximize
z = 11x + 5y
subject to the constraints
3x + 2y ≤ 25
x + y ≤ 10
x ≥ 0, y ≥ 0.
Consider a set of rectangular cartesian axes OXY in the plane.
It is clear that any point which satisfies x ≥ 0, y ≥ 0 lies in the first quadrant.
Now we draw the graph of 3x + 2y = 25
For x = 0, 2y = 25 or 
For y = 0, 3x = 25 or 
Again we draw the graph of x + y = 10
For x = 0, y = 10
For y = 0, x = 10
∴ line meets OX in B (10, 0) and OY in M (0, 10).
Since feasible region is the region which satisfies all the constraints
∴ OACM is the feasible region and corner points are
At 
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