Solve Calculus Problem: Find Max Profit of The Sound of Music Tickets

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    Calculus
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Homework Help Overview

The problem involves maximizing profit from ticket sales for performances of The Sound of Music, given a specific pricing and attendance model. It is situated within the context of calculus, particularly focusing on optimization techniques.

Discussion Character

  • Exploratory, Mathematical reasoning, Problem interpretation

Approaches and Questions Raised

  • The original poster attempts to define functions for attendance and ticket pricing but expresses uncertainty about incorporating expenses and deriving a profit function. Some participants question the definitions of expenses and profit, while others propose a potential profit equation based on attendance and ticket price.

Discussion Status

The discussion is ongoing, with participants exploring different interpretations of the problem and attempting to clarify the relationships between ticket price, attendance, and expenses. Some guidance has been offered regarding the formulation of profit, but no consensus has been reached on the correct approach.

Contextual Notes

Participants are working under the constraints of a homework assignment, which may limit the information they can use or the methods they can apply. There is also a noted challenge in understanding optimization problems in general.

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Homework Statement


Currently 2000 people attend performances of The Sound of Music if tickets cost $40. Expenses are $8 per person in attendance for each performance. For each $2 decrease in the ticket price, 200 more people attend. Calculate the ticket price that produces maximum profit.



Homework Equations



don't really know of relevant equations besides derivatives.

The Attempt at a Solution



So I'm struggling to solve this one, I've been trying to use another similar problem to help me solve this and so i have come up with 2 functions for it.

2000+200x for how much people will come in
40-2x for the minimum price for the fare
now i don't know where to put $8 and well i just can't figure out the main function so i can come up with a derivative and solve for x.
 
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What are expenses when n people attend?

What is profit?
 
well i think the expences will be 8 dollars per person so 8(2000+200x)
the profit before expenses will be... (40-2x)(2000+200x) ??
so overall profit will be mmm P = (40-2x)(2000+200x)-8(2000+200x) ?

man, optimization problems are so tricky...but i can't give up, worth a lot of marks hahaha.
 
I can be missing something, but so far looks OK to me.
 

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