Question: how to find the maximum value of the implicit function

Hi;

Trying to find the maximum values of the implicit function.. I tree the following commands.

 

l:=1:alpha:=1:b:=100:k:=20:

(alpha+(l+alpha)*u+alpha*k*u^2)*a=u*(alpha+(l+alpha)*u+alpha*k*u^2)*(1+l*alpha*b/((alpha+(l+alpha)*u+alpha*k*u^2)));

with(plots):

implicitplot((alpha+(l+alpha)*u+alpha*k*u^2)*a=u*(alpha+(l+alpha)*u+alpha*k*u^2)*(1+l*alpha*b/((alpha+(l+alpha)*u+alpha*k*u^2))),a=0..100,u=0..20,numpoints=9000000,color=black,axes=boxed,font=[1,1,18],thickness=2,tickmarks=[3,3],view=[0..12,0..12],labels=[a,u]);

maximize((alpha+(l+alpha)*u+alpha*k*u^2)*a=u*(alpha+(l+alpha)*u+alpha*k*u^2)*(1+l*alpha*b/((alpha+(l+alpha)*u+alpha*k*u^2))), N=0.5..1, location);

Any help I'll appriciated 

 

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