Fortuner, the latest SUV by Toyota Motors, consumes diesel at the rate of 1400×[1000x+x]1400×[1000x+x] litres per km, when driven at the speed of xx 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?  Choose the correct answer.
A) 30 km per hour
B) 32 km per hour
C) 49 km per hour
D) 54 km per hour
E) 65 km per hour
Given that the diesel consumption is at the rate   1400×[1000x+x]1400×[1000x+x]   Cost of diesel = Rs 35 per litre   Payment to the driver = Rs 125 per hour.   Also given that the SUV is driven at the speed of xx km per hour.   Total cost (c)(c)   =1400×[1000x+x]×800×35+125×800x=1400×[1000x+x]×800×35+125×800x   =70000x+70x+100000x=70000x+70x+100000x   Now differentiating both sides in the above equation with respect to xx.   dcdx=−170,000x2+70=0dcdx=−170,000x2+70=0   ⇒ x=49 km per hour.   49 km per hour
<result>C</result>
Fortuner, the latest SUV by Toyota Motors, consumes diesel at the rate of 1400×[1000x+x]1400×[1000x+x] litres per km, when driven at the speed of xx 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?