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