Maximization problems

• To: mathgroup at smc.vnet.net
• Subject: [mg96686] Maximization problems
• From: replicatorzed at gmail.com
• Date: Fri, 20 Feb 2009 05:48:46 -0500 (EST)

```Dear Group,

consider a toy function 'func' of 6 parameters, and a set of
constraints 'cons' for this function:

In[45]:= func[b_, m_, s_, a_, n_, r_] := Total[{b, m, s, a, n, r}];
cons[b_, m_, s_, a_, n_, r_] :=
And[3 <= a <= 10, 1 <= n <= 10, 1 <= r <= n, 3 <= b <= 10,
1 <= m <= b, 1 <= s <= m, Binomial[b, m] <= a^n];

In[47]:= NMaximize[{func[b, m, s, a, n, r],
And[cons[b, m, s, a, n, r]]
}, {b, m, s, a, n, r}]

Out[47]= {60., {b -> 10., m -> 10., s -> 10., a -> 10., n -> 10.,
r -> 10.}}

In[48]:= Maximize[{func[b, m, s, a, n, r],
And[cons[b, m, s, a, n, r]]
}, {b, m, s, a, n, r}]

Out[48]= Maximize[{a + b + m + n + r + s,
3 <= a <= 10 && 1 <= n <= 10 && 1 <= r <= n && 3 <= b <= 10 &&
1 <= m <= b && 1 <= s <= m && Binomial[b, m] <= a^n}, {b, m, s, a,
n, r}]

While NMaximize gives the correct answer, Maximize is returned
unevaluated. If I remove the last constraint from cons, then Maximize
succeeds as well. Now why is it, that the symbolic method can't
maximize the function? Any idea?

Istvan Zachar

```

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