(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

A truck driving over a flat interstate at a constant rate of 50 mph gets 4 miles to the gallon. Fuel costs $0.89 per gallon. For each mile per hour increase in speed, the truck loses a tenth of a mile per gallon of its mileage. Drivers get $27.50 per hour in wages, and the fixed costs for running the truck amount to $11.33 per hour. What constant speed, between 50 mph and 65 mph, should the dispatcher require on a straight run through 260 miles of Kansas interstate to minimize the total cost of operating the truck?

2. Relevant equations

50 mph for 4 miles/gallon $0.89/gallon cost

1 mph increase in speed --> -(1/10) decrease in mile/gallon mileage

$27.50/hr drivers' wages + $11.33/hr cost to operate = $38.83/hr cost (cost goes up with time)

38.83 = dc/dt ?

3. The attempt at a solution

We're looking for optimum cost (C), I think.

I am really stumped with a system of equations for this one.

I could probably go a lot further with this one on my own if I just had a place to start. Does anyone have any enlightening thoughts?

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# Homework Help: Optimization - help needed setting up a system of equations?

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