Answer:
[tex]x = 60 mph[/tex]
Explanation:
Given that the operating cost is
[tex]c = 12 + \frac{x}{6}[/tex] cents per mile
total miles covered is given as
[tex]d = 400 miles[/tex]
so total cost of drive is given as
[tex]C = (12 + \frac{x}{6})(4)[/tex] $
time taken by the truck to move the distance is given as
[tex]t = \frac{400}{x}[/tex]
So total earnings of the driver is given as
[tex]E = \frac{400}{x} \times 6[/tex] $
now total profit of the driver is given as
[tex]P = \frac{2400}{x} - (48 + \frac{2x}{3})[/tex] $
to maximize the profit we have
[tex]\frac{dP}{dx} = 0[/tex]
[tex]-\frac{2400}{x^2} + \frac{2}{3} = 0[/tex]
so we have
[tex]x = 60 mph[/tex]
