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Question
The profit ₹ y accumulated in thousand in x months is given by y = -x2 + 10x – 15. Find the best time to end the project.
Solution
y = -x2 + 10x – 15
⇒ y = -[x2 – 10x + 52 – 52 + 15]
⇒ y = -[(x – 5)2 – 10]
⇒ y = 10 – (x – 5)2
⇒ (x – 5)2 = -(y – 10)
This is a parabola which is open downwards.
Vertex is the maximum point.
∴ Profit is maximum when x – 5 = 0 (or) x = 5 months.
After that profit gradually reduces.
∴ The best time to end the project is after 5 months.
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