Example 3: Exercise #19 (Section 15.8, p. 675))

> f := l*w + 2*l*h + 2*w*h;

f := l*w+2*l*h+2*w*h

> g := l*w*h-256;

g := l*w*h-256

>

> fl := diff( f, l );

fl := w+2*h

> fw := diff( f, w );

fw := l+2*h

> fh := diff( f, h );

fh := 2*l+2*w

> gl := diff( g, l );

gl := w*h

> gw := diff( g, w );

gw := l*h

> gh := diff( g, h );

gh := l*w

>

> LE := fl=lambda*gl, fw=lambda*gw, fh=lambda*gh;

LE := w+2*h = lambda*w*h, l+2*h = lambda*l*h, 2*l+2...

> LEsol := solve( {LE,g=0}, {l,w,h,lambda} );

LEsol := {w = 8, lambda = 1/2, h = 4, l = 8}, {w = ...
LEsol := {w = 8, lambda = 1/2, h = 4, l = 8}, {w = ...

> LEsol2 := map( allvalues, {LEsol} );

LEsol2 := {{w = 8, lambda = 1/2, h = 4, l = 8}, {w ...
LEsol2 := {{w = 8, lambda = 1/2, h = 4, l = 8}, {w ...

>

> sol2 := {seq( eval( [l,w,h], s ), s=LEsol2 )};

sol2 := {[8, 8, 4], [-4+4*I*sqrt(3), -4+4*I*sqrt(3)...

>