Suppose that the cost for a truck driver is $16.75 per hour and that the cost to

Question

Suppose that the cost for a truck driver is $16.75 per hour and that the cost to operate the truck is v2/46000 per mile where v is the average speed of the truck. How fast should you recommend your driver to drive in order to minimize the total costs?

Hint: Convert problem to Total Cost per Mile for Truck Driver and the Truck

        The Cost per Mile for the Truck Driver will be $16.75 per hour divided by the number of miles driven in an hour which in this case would be v

        The Cost per Mile for the Truck itself is given as v2/46000

Explanation / Answer

for speed v ..

time take to cover 1 mile = 1/v hr

cost of dirver per mile = $ 16.75 / v   per mile

so total cost per mile (T)= 16.75 /v + v^2 / 46000  

dT / dv = - 16.75 / v^2 + 2v / 46000 = 0

so, v^3 = 16.75 * 23000

v = 72.764 miles / hr

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