Question

Rahul is at the whole sale market to purchase folding tables and chairs, to later sell them at his furniture shop. He has only ₹ 5,760 to spend and his van has space to carry at the most 20 items. A table costs him ₹ 360 and a chair costs ₹ 240. Back at his shop, he plans to sell a table at a profit of ₹ 22 and a chair at a profit of ₹ 18. Given that he can sell all the items that he purchases, how many tables and chairs shall he purchase in order to maximise his profit?

Answer 1

Let the number of tables and chairs be x and y respectively

(Max profit) Z = 22x + 18y

Subject to constraints: 

x + y ≤ 20

3x + 2y ≤ 48

x, y ≥ 0

The feasible region OABCA is closed (bounded)

Buying 8 tables and 12 chairs will maximise the profit