We are to minimise
Z = 200x + 500 y
subject to the constraints
x + 2y ≥ 10
3x + 4y ≤ 24
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 the line x + 2y = 10
For x = 0, 2 y = 10 or y = 5
For y = 0, x = 10
∴ line meets OX in A(10, 0) and OY in L(0, 5).
Let us draw the graph of the line 3x + 4y = 24
For x = 0, 4 y = 24 or y = 6
For y = 0, 3x = 24 or x = 8
∴ line meets OX in B(8, 0) and OY in M(0, 6)
Since feasible region is the region which satisfies all the constraints.
∴ CML is the feasible region, which is bounded.
The comer points are C(4, 3), M(0, 6), L(0, 5).
At C(4, 3), Z = 800 + 1500 = 2300
At M(0, 6), Z = 0 + 3000 = 3000
At L(0, 5), Z = 0 + 2500 = 2500
∴ minimum value = 2300 at (4, 3).
