A car is to be driven 200kms on a highway at an uniform speed of x km/hrs (speed Rules of the high way require 40 ≤ x ≤ 70 ). The cost of diesel is Rs 30/litre and is consumed at the rate of 100 + 60

Question

A car is to be driven 200kms on a highway at an uniform speed of x km/hrs (speed Rules of the high way require 40 ≤ x ≤ 70 ). The cost of diesel is Rs 30/litre and is consumed at the rate of 100 + 60 x 2 ​ litres per hour. If the wage of the driver is Rs 200 per hour then the most economical speed to drive the car is

TestHub · Accepted Answer

Let the cost incurred to travel 200 km be $C (x)$ . Then:

$C (x) = (100 + \frac{x ^{2}}{60}) \frac{200}{x} \times 30 + 200 \times \frac{200}{x}$

$= \frac{640000}{x} + 100 x$

This implies that $C^{'} (x) < 0$ for $x \in [40, 70]$ .

Therefore, $C (x)$ is minimum for $x = 70$ in the interval $x \in [40, 70]$ .

Mathematics - Application of Derivative Question with Solution | TestHub

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