Re: Tricky visualization of maximization problem

*To*: mathgroup at smc.vnet.net*Subject*: [mg71009] Re: Tricky visualization of maximization problem*From*: Jean-Marc Gulliet <jeanmarc.gulliet at gmail.com>*Date*: Sat, 4 Nov 2006 23:07:03 -0500 (EST)*Organization*: The Open University, Milton Keynes, UK*References*: <eihm95$ov4$1@smc.vnet.net>

Uwe Ziegenhagen wrote: > Hi, > > I want to maximize > > x1^2 + 4*x1*x2 + 3*x2^2 (eq.1) > > under the constraint > > x1^2 + x2^2 == 1 (eq. 2) > > So far no problem, Maximize gives me 2 + sqrt(5) > > But how can I display this visually? > > For eq. 1 I can use Plot3D[], for eq. 2 ImplicitPlot[] but how to have > them in one picture? > > > Thanks in advance, > > > Uwe > DisplayTogether will plot both graphs. eq1 = x1^2 + 4*x1*x2 + 3*x2^2; eq2 = x1^2 + x2^2; Maximize[{eq1, eq2 == 1}, {x1, x2}] << "Graphics`Graphics`" g1 = Plot3D[eq1, {x1, -2, 2}, {x2, -2, 2}]; g2 = Plot3D[eq2, {x1, -2, 2}, {x2, -2, 2}]; DisplayTogether[g1, g2]; DisplayTogether[g1, g2, PlotRange -> All]; Regards, Jean-Marc