
Re: Maximize a single variable and solve for the rest
Posted:
May 21, 2011 6:44 AM


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

