Question

Assume that the operating cost of a certain truck (excluding driver's wages) is 12+x/6 cents per mile when the truck travels at x mi/hr. If the driver earns $6 per hour, what is the most economical speed to operate the truck on a 400 mi turnpike where the minimum speed is 40 mph and the maximum speed is 70 mph?

Answer 1

Answer:

$x = 60 mph$

Explanation:

Given that the operating cost is

$c = 12 + \frac{x}{6}$ cents per mile

total miles covered is given as

$d = 400 miles$

so total cost of drive is given as

$C = (12 + \frac{x}{6})(4)$ $

time taken by the truck to move the distance is given as

$t = \frac{400}{x}$

So total earnings of the driver is given as

$E = \frac{400}{x} \times 6$ $

now total profit of the driver is given as

$P = \frac{2400}{x} - (48 + \frac{2x}{3})$ $

to maximize the profit we have

$\frac{dP}{dx} = 0$

$-\frac{2400}{x^2} + \frac{2}{3} = 0$

so we have

$x = 60 mph$