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Question
The owner of a milk store finds that, he can sell 980 litres of milk each week at Rs 14/litre and 1220 litres of milk each week at Rs 16/litre. Assuming a linear relationship between selling price and demand, how many litres could he sell weekly at Rs 17/litre?
Solution
Assuming L (litres) along x-axis and R(rupees) along y-axis, we have two points (980, 14) and (1220, 16).
By two point form, the point (L, R) satisfies the equation.
`"y" - 980 = (1220 - 980)/(16 - 14) (x - 14)`
= y - 980 = `240/2 (x - 14)`
y - 980 + 120 (x – 14)
i.e., y = 120 (x - 14) + 980
When x = Rs. 17/litre,
y = 120 (17 - 14) + 980
= y 120 × 3 + 980 = 360 + 980 = 1340
Thus, the owner of the milk store could sell 1340 litres of milk weekly at Rs. 17/litre.
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