A furniture dealer deals in the sale of only tables and chairs. He has Rs. 5000 to invest and a space to store at most 60 pieces. A table costs him Rs. 250 and a chair Rs. 50. He can sell a table at a profit of Rs. 50 and a chair at a profit of Rs. 15. Assuming that he can sell all the items that he buys, how should he invest his money in order that he may maximise his profit?

Let x be the number of tables and y be the number of chairs.
Let Z be the profit
∴    We are to maximize
Z = 50x + 15y subject to the constraints
250x + 50y ≤ 5000
x + y ≤ 60
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.
Let us draw the graph of 250 x + 50y = 5000
For x = 0, 50 y = 5000 ⇒ y = 100
For y = 0, 250 x = 5000 ⇒ x = 20
∴ line 250 x + 50 y = 5000 meets OX in A (20, 0) and OY in B (0, 100)
Again we draw the graph of the line x + y = 60
For x = 0, y = 60
For y = 0, x = 60
∴ line x + y = 60 meets OX in C (60, 0) and OY in D (0, 60).
Since feasible is the region which satisfies all the constraints
∴ feasible region is the quadrilateral OAED. The comer points are O (0, 0). A (20, 0), E (10, 50), D (0, 60)

At O (0, 0), Z = 0 + 0 = 0
At A (20, 0), Z = 50 (20) + 15 (0) = 1000 + 0 = 1000
At E(10, 50), Z = 50 (10) + 15 (50) = 500 + 750= 1250
At D(0, 60), Z = 50 (0) + 15 (60) = 0 + 900 = 900
∴  maximum value of Z = 1250 at E (10, 50)
∴  maximum profit = Rs. 1250
when x = 10, y = 50 i.e., when number of tables = 10, number of chairs = 50