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Calculus/Minimum Optimization

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Expert: Alon Mandes - 4/13/2009


Question
A square bottomed box with no top has a volume of 500 cubic feet. What dimensions minimize the surface area?

Answer
Surface Area S=x²+4xy , where x is the length of the base , & y is
the hieght of the sides. We also know that the volume is 500, thus yx²=500 -> y=500/x². Hence, S=x²+4x*500/x²=x²+1000/x .
To find optimization, we derive S with respect to x , & set S'=0 :
S'=2x-1000/x²
S'=0 -> 2x=1000/x² -> 2x³=1000 -> x=10/1.259=7.95 -> y=7.91

Alon.

Calculus

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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 .

Experience

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".

Organizations
Hi-Tech company : GSM4VOIP ; job possition : Algorythm developer.

Education/Credentials
M.A in Mathematics & Bs.c in Electronics.

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