Re: Maximize function question
- To: mathgroup at smc.vnet.net
- Subject: [mg46254] Re: Maximize function question
- From: drbob at bigfoot.com (Bobby R. Treat)
- Date: Thu, 12 Feb 2004 22:46:14 -0500 (EST)
- References: <c0fru2$c03$1@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
Try this for locating possible extrema:
grad[f_] := (D[f, #1] & ) /@ {k, l}
obj = a*k + w*l;
condition = q == Sqrt[k] + Sqrt[l];
lagrange = obj + lambda*Subtract @@ condition
Append[Thread[grad[lagrange] == 0], condition]
Simplify[First[Solve[%, {k, l, lambda}]]]
PowerExpand /@ %
Simplify[%]
Bobby
"David" <nospam at nospam.com> wrote in message news:<c0fru2$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.