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.