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Question
A furniture dealer deals in tables and chairs. He has ₹ 1,50,000 to invest and a space to store at most 60 pieces. A table costs him ₹ 1500 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 ₹ 1500 and that of each chair is ₹ 750, the total cost of x tables and y chairs is 1500x + 750y. Since the dealer has ₹ 1,50,000 to invest, 1500x + 750y ≤ 1,50,000 = 2x + y ≤ 200
Hence the system of inequations are
x + y ≤ 60, 2x + y ≤ 200
First we draw the lines AB and CD whose equations are
x + y = 60 and 2x + y = 200, x ≥ 0, y ≥ 0 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 | 2x + y = 200 | C(100,0) | D(0,200) | ≤ | origin side of line CD |
The feasible solution is shaded in the graph.
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