# Cutting Cost

**Calculus**Level 4

A taxi is driving \(200 \) kilometers on a highway at a uniform speed of \(x\ \text{km/hr}\) (speed rates of highway requires \(40\leq x \leq 70\)). The cost of fuel is \($30 \) per litre and is consumed at the rate of \(\left ( 100+\dfrac{x^2}{60} \right ) \) liter per hour. If the wage of the driver is \( \ $200 \) per hour then what will be the most economical speed to drive the taxi?

**Details and Assumptions**

Most economical refers to maximum profit or minimum loss. (As per the point of view of driver)

\( \text{ Profit or Loss } \ = \ \mid \text{ Wage earned - Price of fuel } \mid \)