Question

The cost of an overhaul of an engine is ₹ 10,000 The operating cost per hour is at the rate of 2x – 240 where the engine has run x km. Find out the total cost if the engine runs for 300 hours after overhaul

Answer 1

Given that the overhaul cost is ₹ 10,000.

The marginal cost is 2x – 240

MC = 2x – 240

C = `int "MC"  "d"x + "k"`

C = x² – 240x + k

k is the overhaul cost

⇒ k = 10,000

So C = x² – 240x + 10,000

When x = 300 hours, total cost is

C = (300)² – 240(300) + 10,000

⇒ C = 90,000 – 72000 + 10,000

⇒ C = 28,000

So the total cost of the engine run for 300 hours after the overhaul is ₹ 28,000.