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showResetIcon = "false" showAnimationButton = "true" enableRightClick = "false" errorDialogsActive = "true" enableLabelDrags = "false" showMenuBar = "false" showToolBar = "false" showToolBarHelp = "false" showAlgebraInput = "false" useBrowserForJS = "true" allowRescaling = "true" />
  
==Visualisiserung mit Tabelle==
+
==Visualisiserung zur Überprüfung der Ergebnisse==
 +
Bewege den roten Punkt, um die Größe zu verändern.
 
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Version vom 31. Januar 2012, 21:05 Uhr

Inhaltsverzeichnis

Problemstellung

Der Goldfisch in Wermelskirchen möchte wiedereröffnen. Da es sich um einen Raucher-club handeln soll, hat der neue Inhaber sich überlegt, Streichholzschachteln als Werbung zu nutzen. Den Großteil seines Geldes hat er bereits in die Sanierung gesteckt, deshalb will er die Streichholzschachteln von seinen Mitarbeitern basteln lassen und zwar mit möglichst wenig Materialverbrauch. In einem Großmarkt hat der Besitzer dementspre-chend Pappe und Streichhölzer (4,5cm lang) gekauft. Einer der Mitarbeiter kam gestern mit folgender Bastelanleitung zu mir:

(Siehe Aufgabenblatt)

Er fragte mich, wie er aus der Pappe möglichst viele Streichholzschachteln basteln könnte. Als Vorgabe hat er gesagt bekommen, dass das Volumen 45cm³ haben muss. Könnt ihr ihm helfen, herauszufinden, welche Maße die Streichholzschachtel haben muss? (Die Klebekanten [siehe gestrichelte Linien] werden für die Berechnung nicht weiter berücksichtigt)

Falls du nicht weiterkommst: Hier findest du Hilfen

Hauptbedingung

 O=15a+20b+4ab

Nebenbedingung

 45=5ab

Zielfunktion

 O(a)=15a+180/a+36

Ableitung

 O'(a)=15+180/a^2

Notwendige Bedingung

 0=15+180/a^2

 a=3,46cm


Hinreichende Bedingung

 O''(3,46)>0 --> Tiefpunkt

Seitenlänge b und Oberfläche O

 b=2,6cm

 O=139,9cm^2

Randextrema

Sowohl fuer a gegen 0 als auch fuer a gegen unendlich, geht O(a) 
gegen unendlich --> 3,46 ist ein globales Minimum

Visualisierung zur Überprüfung der Ergebnisse

Bewege den roten Punkt, um die Groesse der Schachtel zu verändern

Visualisiserung zur Überprüfung der Ergebnisse

Bewege den roten Punkt, um die Größe zu verändern.

Weiterführende Problemstellung

Bastel eine "optimale" Streichholzschachtel.

Überlege: Warum sind Streichholzschachteln in der Realität nicht "optimal"?

Verfasser

Team.gif
Entstanden unter Mitwirkung von:

Janina Wittenstein