Re: LOGO-L> Solving a Max Problem Using Logo

[dajoy@hoy.net]

From:           	Yehuda <yehuka@softhome.net>
> To solve min-max problems we need usually calculus. But if we have Logo,  we can
> solve this sort of problems, with much younger students.

I'm not sure if I used calculus:

make "f [(30-2*:x)*(30-2*:x)*:x]
show intervalsolve [deriv :f "x :x] "x 0 10
[0 10]
[7.49999999833904 0]
[5.99999999988195 7.49999999833904]
[5.35714285244459 5.99999999988195]
[5.12195121721646 5.35714285244459]
[5.04098360180739 5.12195121721646]
[5.01369863231258 5.04098360180739]
[5.00457038462791 5.01369863231258]
[5.00152392622646 5.00457038462791]
[5.0005080260684 5.00152392622646]
[5.00016934403484 5.0005080260684]
[5.00005644794088 5.00016934403484]
[5.00001881619279 5.00005644794088]
[5.00000627272929 5.00001881619279]
[5.00000209157829 5.00000627272929]
[5.00000069449318 5.00000209157829]
[5.00000022585075 5.00000069449318]
[5.00000007174192 5.00000022585075]
[5.00000002753037 5.00000007174192]
[5.00000000605619 5.00000002753037]
[5.00000000605619 5.00000000605619]
[5.00000000352982 5.00000000605619]
[5.00000000479301 5.00000000352982]
[5.00000000384562 5.00000000479301]
[5.00000000408246 5.00000000384562]
[5.00000000392457 5.00000000408246]
[5.00000000388509 5.00000000392457]
[5.00000000390483 5.00000000388509]
[5.00000000389167 5.00000000390483]
[5.00000000388838 5.00000000389167]
[5.00000000389003 5.00000000388838]
[5.00000000389085 5.00000000389003]
[5.0000000038903 5.00000000389085]
[5.00000000389016 5.0000000038903]
[5.00000000389007 5.00000000389016]
[5.00000000389005 5.00000000389007]
[5.00000000389003 5.00000000389005]
[5.00000000389003 5.00000000389003]
[5.00000000389003 5.00000000389003]
[5.00000000389003 5.00000000389003]
[5.00000000389003 5.00000000389003]
5.00000000389003

to deriv :func :dep :depv
localmake "inf 0.0000005
op ((eval :func :dep :depv+:inf)-(eval :func :dep :depv-:inf))/(2*:inf)
end

to eval :func :dep :depv
localmake :dep :depv
op run :func
end 

to intervalSolve :func :dep :ini :fin

local [lower upper depLower depUpper currentAns lastAns depCurrent]

make "lower :ini
make "upper :fin

make "currentAns :ini
make "lastAns :fin

make "depLower eval :func :dep :lower
make "depUpper eval :func :dep :upper

if (not (:depLower * :depUpper) < 0) [print [Interval useless]]

while [not :currentAns = :lastAns] [
show list :currentAns :lastAns
	make "lastAns :currentAns 
	make "currentAns :lower - :depLower * (:lower - :upper) / (:depLower - :depUpper)
	make "depCurrent eval :func :dep :currentAns
	ifelse (:depUpper * :depCurrent < 0) [
		make "lower :currentAns
		make "depLower :depCurrent
	] [
		make "upper :currentAns
		make "depUpper :depCurrent
	]
]
op :currentAns
end


I guess intervalSolve, numInt (posted earlier), deriv, and eval put together could be 
a useful set of tools.


---------------------------------------------------------------
Please post messages to the Logo forum to logo-l@gsn.org.  Mail
questions about the list administration to logofdn@gsn.org.  To
unsubscribe send    unsubscribe logo-l    to majordomo@gsn.org.