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July 22, 2025, 06:29:45 pm
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Author Topic: Lagrange Multipliers Question!  (Read 1107 times)  Share 

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QuantumJG

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Lagrange Multipliers Question!
« on: August 14, 2010, 11:31:39 am »
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Lagranges multipliers question!

Design a cylindrical can with a lid to contain 1L of water, using the minimal amount of metal.

Here's how I tackled it.

S(r,h) = 2πrh + πr2
V(r,h) = πr2h - 1 = 0

So

Let gradS = λgradV

So (2πh + 2πr, 2πr) = λ(2πrh,πr2)

So

πr2h - 1 = 0 ...1
h + r = λrh ...2
2 = λr ...3 because r can't be zero!

Anyway I got r = h = (π)-3

But according to the book it's wrong!
« Last Edit: August 14, 2010, 11:47:39 am by QuantumJG »
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