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Question
Mr. Rajesh. Has Rs. 1800 to spend on fruits for a meeting. Grapes cost Rs. 150 per kg. and peaches cost Rs. 200 per kg. Formulate and solve it graphically.
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Solution
The cost of grapes = Rs. 150/- per kg.
Let x kg of grapes be bought.
Then total cost of grapes = 150 x
The cost of peaches = Rs.200/- per kg.
Let y kg of peaches be bought.
Then total cost of peaches = 200 y
Since Mr. Rajesh has total amount Rs. 1800 to spend on fruits.
His total expenses 150 x + 200 y should be less than or equal to 1800.
Inequation is 150x + 200y ≤ 1800
⇒ 3x + 4y ≤ 36 ......(i)
x, y ≥ 0 as the quantities of grapes and peaches can’t be negative.
Points on axes are
| x | 12 | 0 |
| y | 0 | 9 |
(12, 0) on X-axis and (0, 9) on Y-axis.
Since origin satisfies the inequation, solution set is towards origin.
Since x and y are both positive, the solution lies in the first quadrant only.
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