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Calculus/what are the two equations?
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Question
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 (mph). The driver is paid $10.00 per hour. Find the speed that minimizes the cost of a 110-mile trip. (assume there are no other costs).
the Total coast is compound of : fuel coast (per hour) + driver coast (per hour) .
The distance is 110 miles, with velocity v . Therefore the duration of the journey is :
t=110/v .
Fuel_Coast=[vē/360]$*t=[vē/360]*[110/v]=11v/36 .
Driver_Coast=10$*t=10*[110/v]=1100/v .
T(v)=[11(v)/36]+[1100/(v)]. To find minimum we derive T(v).
T'(v)=[11/36]-[1100/(vē)]
Now we solve T'(v)=0 :
11/36]=1100/vē
v=60 mph .
Alon.
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Answers by Expert:
Alon Mandes
Expertise
Kind of questions I can answer : Limits, Derivatives, Integration, Implicit functions, continuousity, differentiation ,Extremum problems, Lagrange multipliers, Gradients, Surface integrals, Multi variables functions ,Multi variables Integrals,Complex variables ,Complex functions, Curves, Trajectory integrals & Vector analyse,Divergence,Rotor & word problems. Kind of question I can't answer : Economics,Combinatorics,infinite series & convergence ,Statistics & Probabilities .
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1. I'm a team member of mathnerds (math site for answering questions)
2. I'm a team member in the Student's Union of the Technion, helping
students who have problems in mathematics.
3. 2 years of experience as a math teacher in college.
4. I give free homework help for high school students in
Mathematics & Physics.
5. I teach part time in collage the subjects : "Digital Signal Processing" , "Random Signals & Noise" ,
"Complex Functions".
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Hi-Tech company : GSM4VOIP ; job possition : Algorythm developer.
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M.A in Mathematics & Bs.c in Electronics.
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