A furniture dealer deals in tables and chairs. He has ₹ 15,000 to invest and a space to store at most 60 pieces. A table costs him ₹ 150 and a chair ₹ 750. Construct the inequations and find the feasible solution.

#### Solution

Let x be the number of tables and y be the number of chairs. Then x ≥ 0, y ≥ 0.

The dealer has a space to store at most 60 pieces. ∴ x + y ≤ 60

Since, the cost of each table is ₹ 150 and that of each chair is ₹ 750, the total cost of x tables and y chairs is 150x + 750y. Since the dealer has ₹ 15,000 to invest, 150x + 750y ≤ 15000

Hence the system of inequations are

x + y ≤ 60, 150x + 750y ≤ 15000, x ≥ 0, y ≥ 0.

First we draw the lines AB and CD whose equations are

x + y = 60 and 150x + 750y = 15000 respectively.

Line |
Equation |
Points on the X-axis |
Points on the Y-axis |
Sign |
Region |

AB | x + y =60 | A(60,0) | B(0,60) | ≤ | origin side of line AB |

CD | 150x + 750y = 15000 | C(100,0) | D(0,20) | ≤ | origin side of line CD |

The feasible solution is OAPDO which is shaded in the graph.