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.