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Calculus/Optimization Problem
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Question
A dairy farmer plans to enclose a rectangular pasture adjacent to a river. To provide enough grass for the herd, the pasture must contain 245,000 square meters. No fencing is required along the river. What dimensions will use the least amount of fencing?
Ok, let's set x & y are the dimensions of the fence. Then the
perimeter of the rectangular fencing will be f=2x+y. ("Note that
y instead of 2y because the river side do not require fencing").
Ok, we also know that the area of the rectangular is 245,000 .
That means xy=245,000 -> y=(245,000)/x. Let's put this in our
optimization function f : f=2x+(245,000)/x. Now, we derive f & set
it equal to zero : f'=2-(245,000)/x^2. ("Note that [1/x]'=-1/x^2").
f'=0 --> 2=245000/x^2 --> x^2=122500 --> x=350 meters. That means
y=(245,000)/350=700 meters.. & these are the optimal dimensions for
least amount of fencing.
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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