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MathGroup Archive 2004

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Re: Maximize function question

  • To: mathgroup at smc.vnet.net
  • Subject: [mg46355] Re: Maximize function question
  • From: drbob at bigfoot.com (Bobby R. Treat)
  • Date: Mon, 16 Feb 2004 08:59:55 -0500 (EST)
  • References: <c0fru2$c03$1@smc.vnet.net> <c0hhpk$lg0$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

That really should be

grad[f_, vars_] := (D[f, #1] & ) /@ vars
obj = a*k + w*l; 
condition = q == Sqrt[k] + Sqrt[l]; 
lagrangian = obj + lambda*Subtract @@ condition
vList = {k, l, lambda}; 
Thread[grad[lagrangian, vList] == 0]
First[Solve[%, vList]]
Simplify[%, q > 0]
Simplify@PowerExpand@%

Bobby

drbob at bigfoot.com (Bobby R. Treat) wrote in message news:<c0hhpk$lg0$1 at smc.vnet.net>...
> Try this for locating possible extrema:
> 
> grad[f_] := (D[f, #1] & ) /@ {k, l}
> obj = a*k + w*l; 
> condition = q == Sqrt[k] + Sqrt[l]; 
> lagrange = obj + lambda*Subtract @@ condition
> Append[Thread[grad[lagrange] == 0], condition]
> Simplify[First[Solve[%, {k, l, lambda}]]]
> PowerExpand /@ %
> Simplify[%]
> 
> Bobby
> 
> "David" <nospam at nospam.com> wrote in message news:<c0fru2$c03$1 at smc.vnet.net>...
> > Hello,
> > 
> > I am attempting to perform a constrained optimization in Mathematica 5.0 on
> > the objective function:
> > 
> > f(K,L)=aK+wL s.t. K^0.5 + L^0.5=Q  where a,w,Q are constant.
> > 
> > I define:
> >     objA[K_,L_]:=rK+wL
> > and
> >     constraintsA = {K^0.5+L^0.5==Q,K>=0, L>=0}
> > 
> > After which I try to evaluate
> > 
> >     Maximize[{objA[K,L],constraintsA},{K,L}]
> > 
> > However, I receive an error message that the objective function contains a
> > nonconstant expression independent of variables {K,L}.
> > 
> > Though the calculation is trivial and is easy to do by hand, I would like to
> > be able to figure out how to do these types of optimization problems not
> > having to assign real numbers to the constants for future use.  Is there an
> > elegent way to do this?
> > 
> > Your collective help is greatly appreciated.


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