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Re: maximization question

• To: mathgroup at smc.vnet.net
• Subject: [mg42825] Re: maximization question
• From: Paul Abbott <paul at physics.uwa.edu.au>
• Date: Wed, 30 Jul 2003 19:30:10 -0400 (EDT)
• Organization: The University of Western Australia
• References: <bfo59o$cg5$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

In article <bfo59o$cg5$1 at smc.vnet.net>,
 "Tun Lin" <tunlin220 at hotmail.com> wrote:

> I try to solve a maximization problem and get stuck at the first step. This 
> step is to maximize a function with four inequality constraints, which I 
> describe in the link following. I first solved the question by hand  (the 
> results are also shown in the link), then tried mathematica. I kept getting 
> error messages as shown and the results are different. What is the problem?
> 
> The question and command line is at:
> 
> http://www.pbase.com/image/19486173/original

Well, the given hand solution to the problem posted there is not correct 
(instead of using the approximate multiplier and power 0.5, I use the 
exact 1/2 instead)! This can be seen as follows:

In[1]:= {
   (1/2)(Sqrt[qH] - tH) + (1/2)(Sqrt[qL] - tL), 
   tL - bL qL >= 0, 
   tH - bH qH >= 0,
   tL - bL qL >= tH - bL qH, 
   tH - bH qH >= tL - bH qL, 
   qL >= 0, qH >= 0, 
   tL >= 0, tH >= 0} /. {bH -> 2, bL -> 20} /.
   {qL -> 1/16, qH -> 1/5776, tL -> 20/5776, tH -> 740/5776}

Out[1]={5/76, False, True, False, True, True, True, True, True}

Clearly tL is less than bL qL!

Cheers,
Paul

-- 
Paul Abbott                                   Phone: +61 8 9380 2734
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