Transportation Costs (or Trucker's Dilemma)

label Algebra
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schedule 1 Day
account_balance_wallet $5

A truck driving 260 miles over a flat interstate at a constant rate of 50 miles per hour goes 7 miles to the gallon. Fuel costs $3.50 per gallon. For each mile per hour increase in speed, the truck loses a tenth of a mile per gallon in its mileage. Drivers get $27.50 per hour in wages and fixed costs for running the truck amount to $11.33 per hour. What constant speed (between 50 mph and the speed limit of 65 mph) should the truck drive to minimize the total cost of the trip?

May 25th, 2015

So overall, the trip is going to take 260 miles/50 mi/hr = 5.2 hrs at that speed.

So driver cost = 27.5*5.2 + 11.33*5.2 = $201.92 at 50 mi/hr

Gas cost: 260/7* $3.5 = $130 @ 50 mi/hr

Total cost @ 50 = $332.92

I only have 20 minutes to calculate this very, very long solution, so this is the ultimate formula for speed:

s = 260/s * 27.5 + 260/s * 11.33 + 260/(12-0.1s)*3.5

This relates cost to speed.


62 miles is the cheapest speed :)


May 25th, 2015

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