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Re: Maximize a single variable and solve for the rest

• To: mathgroup at smc.vnet.net
• Subject: [mg119058] Re: Maximize a single variable and solve for the rest
• From: Bob Hanlon <hanlonr at cox.net>
• Date: Sat, 21 May 2011 06:44:16 -0400 (EDT)

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 at 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