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Question: Interpret 2 symbolic solve solutions when only 1 numerical solution exists?

Question:Interpret 2 symbolic solve solutions when only 1 numerical solution exists?

brian abraham 599 Maple
June 24 2008
0

Download 2129_Minimising.mws
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In the attached file (Minimising) I minimise the following function
((30.*Pv+100.*T+50.*PLu-25.*Pu)^2+PLu^2)^(1/2)+((-100.*T-50.*PLu-29.*Pv+25.*Pu)^2+(Pu-1.*PLu)^2)^(1/2)

by differentiating w.r.t PLu, solving for PLu and then substituting back into the original function. 
 
 
I do this in two ways
 
First: I provide values for Pv, T and Pu, differentiate and then use fsolve and a single value is returned for PLu. I then substitute this Plu value and the same Pv, T and Pu values into the function to get the minimum value at the specified Pv, T and Pu.
 
 
Second: I differentiate without providing values for Pv,T and Pu and then use solve but I get two solutions.
 
If I substitute each solution back into the original function and then provide values for Pv, T and Pu, one solution provides the minimum value and the other does not. 
 
Which solution provides a minimum value seems to vary depending on the values of Pv, T and Pu.
 
Why does Maple find 2 solutions and why do they seem to vary as to which one provides a minumum?
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