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Question
Your company is mass-producing a cylindrical container. The flat portion (top and bottom) costs 3cents per square inch and the curved portion costs 5 cents per square inch. If your budget is$9.00 per container, what dimensions will give the largest volume
Amount of flat portion F=2π*r^2.
Amount of curved portion C=2*π*r*h.
Costs of flat : 3*2*π*r^2=6πr^2.
Costs of curved : 5*2*π*r*h=10πrh.
Total coast per container T=6πr^2+10πrh=9 -> h=[9-6πr^2]/[10πr]->
h=(9/10π)(1/r)-(3/5)r.
We want to maximize volume V : V=πhr^2.
Max { π*[(9/10π)(1/r)-(3/5)r]*r^2 } =
MAx { (9/10)r-(3π/5)r^3 }. Let's derive :
[ (9/10)r-(3π/5)r^3 ]' = 9/10-(9π/5)r^2. Let's set the derivative
equal zero : 9/10-(9π/5)r^2=0 -> 1/√(2π). & h will be :
h=(9/10π)(1/1/√(2π))-(3/5)1/√(2π)=(18π-3)/10π.
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 .
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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