Question
Find the maximum value of f = x + 2 y subject to the constraints:
2x + 3 y ≤ 6
x + 4 y ≤ 4
x, y ≥ 0
Solution
We are to maximize
f = x + 2y
subject to the constraints
2x + 3 y ≤ 6
x + 4 y ≤ 4
x, 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 the line 2 x + 3 y = 6.
For x = 0, 3 y = 6, or y = 2
For y = 0, 2 x = 6, or x = 3
∴ line meets OX in A (3, 0) and OY in L (0, 2)
Let us draw the graph of line x + 4 y = 4
For x = 0, 4 y = 4, or y = 1
For y = 0, x = 4
∴ line meets OX in B (4, 0) and OY in M (0, 1)
Since feasible region is the region which satisfies all the constraints
∴ OACM is the feasible region. The comer points are
At 
