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Symbolic Optimization Problem

• To: mathgroup at smc.vnet.net
• Subject: [mg88502] Symbolic Optimization Problem
• From: "Gonca Senel" <gsenel at bilkent.edu.tr>
• Date: Tue, 6 May 2008 06:46:17 -0400 (EDT)

Dear All,

I need to maximize

\[Pi] = R*\[Alpha] (1/\[Alpha] (\[Beta]/R)^(1/(
1 - \[Beta])) - (1 - \[Gamma])*\[Beta]^(2/(
1 - \[Beta]))*\[Alpha]^(\[Beta]/(
1 - \[Beta]))) - (1/\[Alpha] (\[Beta]/R)^(1/(
1 - \[Beta])) - (1 - \[Gamma])*\[Beta]^(2/(
1 - \[Beta]))*\[Alpha]^(\[Beta]/(1 - \[Beta])))

with respect to R (R will be in terms of alpha, beta and gamma) under the
assumption that beta, alpha and gamma will all be between 0 and 1. How can
I solve this symbolic optimization with Mathematica? I tried to solve it
but I am not very experienced with Mathematica and your help is greatly
appreciated.

Sincerely,

Gonca Senel
Bilkent University