Economic optimization

Topic:
Calculus
Economical optimization Imagine you're selling chocolates at a party. You reckon that no-one will buy them if they are as expensive as 1 € each (or dollars, punds etc). On the other hand you will probably not sell more than 30 even if you give them away. After all, there are only a handful of persons coming to the party. What price should you set so that your profit will be as high as possible? Your parents charge you for using the kitchen table because you make such a mess and you have to buy your ingredients yourself so you don't want to make too many. How to figure this? With mathematics of course.
Study the GeoGebra model and try to understand how each function depends on the others. Play with the sliders and see what happens. Try changing the supply function for another kind of function like S(x) = GiveAwayNumber - 3x^2 or something similar. Investigate how your maximum profit depends on the parameters (sliders). What parameter is your optimum price most sensitive to? What parameter is your maximum profit most sensitive too?