# 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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