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Topic: Maximize a single variable and solve for the rest
Replies: 5   Last Post: May 24, 2011 5:18 AM

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Peter Pein

Posts: 1,147
Registered: 5/4/05
Re: Maximize a single variable and solve for the rest
Posted: May 21, 2011 5:54 AM
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Am 20.05.2011 12:38, schrieb Ramiro:
> Hello,
>
> I have a problem where I would like to solve an equation (namely (h+s+b
> +d==1) with some constraints, while maximizing for a related variable
> "c" (c<=9). Please see below, any suggestions?
>
> r1 = 3/4;
> r2 = 1;
> Block[{h, s, b, d, c},
> NMaximize[{h + s + b + d,
> b == c*r1 && h + s + b + d == 1 && d == c*r2 && h == s &&
> b + d <= 0.9}, {h, s, b, d, c}]]
>
> {1., {h -> 0.5, s -> 0.5, (3 c)/4 -> 0., c -> 0., c -> 0.}}
>
> Should I be using NSolve?
>
> Thanks in advance,
> Ramiro
>

Maybe - or surely! - I misunderstand your question. You've got the
solution in your posting

The only thing to keep in mind is that s >= 1/20:

In[15]:=
Block[{h,s,b,d,c},Reduce[{b==c*r1&&h+s+b+d==1&&d==c*r2&&h==s&&b+d<=9/10},{h},Backsubstitution->True]]
Out[15]= Re[s]>=1/20&&Im[s]==0&&d==-(4/7) (-1+2 s)&&c==-(4/7) (-1+2
s)&&b==-(3/7) (-1+2 s)&&h==s
In[16]:= ToRules[Drop[%,2]]
Out[16]= {d->-(4/7) (-1+2 s),c->-(4/7) (-1+2 s),b->-(3/7) (-1+2 s),h->s}
In[17]:= h+s+b+d/.%
Out[17]= 1

Peter




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