On 13/06/2011 1:08 AM, meri sguanci wrote:
> Hi,
> I'm a noob, so I'm sorry for the stupid question. I started using Maxima
> few days ago 'cause I need it for a project @ university. I have a very
> simple problem: I don't know how to find the minimum of an
> expression on a domain.
> This is what I've done:
>
> /* [wxMaxima: input start ] */
> cmin1:1.1;
> cmin2:1.5;
> cqi1:3;
> cqi2:1;
> xmin1:0.8;
> xmin2:0.85;
> Pnom1:80;
> -Pnom2:120;
> Preq:80;
> /* [wxMaxima: input end ] */
> /* [wxMaxima: input start ] */
> cost1(P1):=P1*(cmin1+cqi1*(P1/Pnom1-xmin1)^2);
> /* [wxMaxima: input end ] */
> /* [wxMaxima: input start ] */
> cost2(P2):=P2*(cmin2+cqi2*(P2/Pnom2-xmin2)^2);
> /* [wxMaxima: input end ] */
> /* [wxMaxima: input start ] */
> COSTOTOT(P1,P2):=cost1(P1)+cost2(P2);
> /* [wxMaxima: input end ] */
> /* [wxMaxima: input start ] */
> plot3d(COSTOTOT(P1,P2),[P1,0,Pnom1],[P2,0,Pnom2]);
> /* [wxMaxima: input end ] */
> /* [wxMaxima: input start ] */
> Costo1v(P1):=cost1(P1)+cost2(Preq-P1);
> /* [wxMaxima: input end ] */
>
> I need to know the minimum of Costo1v with P1 in the range [0,Pnom1].
> How can I do?
>
> Thanks a Lot for ur time and help
>
> Yours,
> Maria Sguanci
>
>
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You have written "-Pnom2:120;". I have taken this to mean
"Pnom2:-120;". If you meant something else then your answers will be
different, but the methodology is the same.
The first thing to do is to plot the expression
plot2d(Costo1v(P1),[P1,0,Pnom1]);
This shows that the function is well-behaved with a minimum near P1 ~ 78.
The global extrema are found at the points where
diff(Costo1v(P1),P1)=0. Don't forget to check for local extrema at the
ends of the domain.
diff(Costo1v(P1),P1);
solve(%,P1);
%,numer;
[P1 = - 29.80284238565096, P1 = 78.49849455956399]
Either by inspection from the graph, or by evaluating
diff(Costo1v(P1),P1,2), you can determine if the extrema a maxima,
minima or inflection points.