Atruck gets 500/x miles per gallon (mpg) when driven at a constant speed of x mph, where 40 ≤ x ≤ 80. if the price of fuel is $2.80/gal and the driver is paid $10/hr, at what speed is it most economical for the trucker to drive? (round your answer to two decimal places.)

Answer :

42.26 mph (approx)

Explanation :

Given,

Fuel consumption = 500/x miles per gallon,

Speed = x miles per hour

Also,  hourly cost = $2.80/gal,

So, fuel cost =

dollar per mile,

The driver earns $10 per hour.

So, labour cost = (10 dollars per hour) × (1/x hr per mile)

dollars per mile,

Thus, total cost,

Differentiating with respect to x

Again differentiating with respect to x,

When,

At x = 42.26, = positive.

Hence, the speed would be 42.26 miles per hour.

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