Cost vs Speed

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mares09

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Jul 11, 2007
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A small business uses a minivan to make deliveries. The cost per hour for fuel is F = (V^2) / 360, where V is the speed of the minivan (in mph). The driver is paid $10 per hour. Find the speed that minimizes the cost of a 110-mile trip. (Assume there are no other costs other than fuel and wages).

What I have been able to figure out so far is that F + 10*T = (V^2) / 360. But I dont know how to relate the distance information that they give me. I know that Im supposed to find the derivative and then the minumun should be my answer, but I just cant figure out how to setup the equation.

Thank you.
 
mares09 said:
A small business uses a minivan to make deliveries. The cost per hour for fuel is F = (V^2) / 360, where V is the speed of the minivan (in mph). The driver is paid $10 per hour. Find the speed that minimizes the cost of a 110-mile trip. (Assume there are no other costs other than fuel and wages).

What I have been able to figure out so far is that

F + 10*T = (V^2) / 360...How-why is that??

First write cost function

C(ost) = Cost of fuel + cost of driver = (V^2/360 + 10)*T ........(1)

Distance = speed * Time (Assuming constant speed)

110 = V * T

T = 110/V ... using this in (1) - we get

C = (V^2/360 + 10)*110/V

Now minimize cost by your favorite method

. But I dont know how to relate the distance information that they give me. I know that Im supposed to find the derivative and then the minumun should be my answer, but I just cant figure out how to setup the equation.

Thank you.
Click to expand...
 
Ok so I have that equation, then what I did is C = (110V / 360) + (1100/V) then I think I have to get the derivative dc/dv = (792V - 396V^2 + 1425600)/ 1296V^2.

Im confused, I dont even know if that derivative is correct I used quotient rule.

Thanks.
 
Well, double check - see if you get same answer.

Does not look correct - differentiate term by term. The answer I get is a "nice" integer and it is greater than 50 and less than 75.

You got time ... the whole week-end...
 
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