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Question:

Fortuner, the latest SUV by Toyota Motors, consumes diesel at the rate of $\frac{1}{400}$ $\{(\frac{1000}{x}) + x\}$ litres per km, when driven at the speed of x km per hour. If the cost of diesel is Rs.35 per litre and the driver is paid at the rate of Rs.125 per hour then find the approximate optimal speed (in km per hour) of Fortuner that will minimize the total cost of the round trip of 800 kms.

Explanation:

Rate of consumption of diesel when speed = x kmph

= $\frac{1}{400}$ $\{(\frac{1000}{x}) + x\}$ litres/km

Diesel cost = Rs. 35 per litre

Driver is paid Rs. 125 per hour

Distance of 800 km

∴ Total cost = $(\frac{800}{x})$ 125 + $\frac{1}{400}$ $\{(\frac{1000}{x}) + x\}$ × 35 × 800

= 800 $[\frac{125}{x} + \frac{1000 + x^{2}}{400 x} \times 35]$

= $\frac{170000 + 70 x^{2}}{x}$

Substituting the options in this, we find that x = 49 gives the minimum cost of Rs. 6899.38

Hence, option (a).

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