Date: May 21, 2011 5:54 AM
Author: Ramiro Barrantes-Reynolds
Subject: Re: Maximize a single variable and solve for the rest

thank you Daniel and Bob, this solved it, please excuse my confusion.

On 5/20/11 6:49 AM, Bob Hanlon wrote:
> It makes no sense to Maximixe the LHS of an equation since it is fixed to be equal to the RHS. Presumably you are trying to maximize the variable c.
>
> r1 = 3/4;
> r2 = 1;
>
> Maximize[{c, b == c*r1, h + s + b + d == 1, d == c*r2, h == s,
> b + d<= 9/10}, {h, s, b, d, c}]
>
> {18/35, {h -> 1/20, s -> 1/20, b -> 27/70, d -> 18/35, c -> 18/35}}
>
> Solve[{b == c*r1, h + s + b + d == 1, d == c*r2, h == s, b + d<= 9/10}, {h,
> s, b, d, c}, Reals] // Quiet
>
> {{h -> ConditionalExpression[1 - (7*c)/4 + (1/2)*(-1 + (7*c)/4),
> c<= 18/35],
> s -> ConditionalExpression[(1/2)*(1 - (7*c)/4), c<= 18/35],
> b -> ConditionalExpression[(3*c)/4, c<= 18/35],
> d -> ConditionalExpression[c, c<= 18/35]}}
>
> Since you want c maximized,
>
> %[[1]] /. c -> 18/35
>
> {h -> 1/20, s -> 1/20, b -> 27/70, d -> 18/35}
>
>
> Bob Hanlon
>
> ---- Ramiro<ramiro.barrantes@gmail.com> wrote:
>
> =============
> 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