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

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In summary, the conversation discusses a problem involving the calculation of maximum profit for performances of The Sound of Music. The problem states that there are currently 2000 attendees at a ticket price of $40, with expenses of $8 per person. It is given that for every $2 decrease in ticket price, 200 more people attend. The conversation includes attempts at solving the problem using functions and derivatives, but the final solution is not reached.
  • #1
the_morbidus
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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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  • #2
What are expenses when n people attend?

What is profit?
 
  • #3
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.
 
  • #4
I can be missing something, but so far looks OK to me.
 

1. How do I find the maximum profit for The Sound of Music tickets using calculus?

To find the maximum profit, you will need to use the derivative of the profit function and set it equal to zero. Then, solve for the variable to find the maximum profit value. This method is known as the "critical point" method.

2. Can I use other methods besides calculus to find the maximum profit?

Yes, there are other methods such as the graphical method and the algebraic method that can also be used to find the maximum profit. However, calculus is often the most efficient and accurate method for solving these types of problems.

3. What information do I need to have in order to solve the calculus problem for finding the maximum profit?

You will need to have the profit function, which is typically given in terms of the number of tickets sold and the ticket price. You will also need to have a good understanding of calculus principles, such as derivatives and critical points.

4. Is it necessary to have a specific knowledge of The Sound of Music in order to solve this calculus problem?

No, you do not need to have any specific knowledge about The Sound of Music to solve this problem. The problem is purely mathematical and can be solved using general calculus principles.

5. Can calculus be used to solve other types of profit maximization problems?

Yes, calculus can be applied to solve various types of optimization problems, including profit maximization. It is a powerful tool for finding the maximum or minimum values of a function, making it useful in many areas of science, economics, and engineering.

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