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)

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


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