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.

Answer 1

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.