anonymous
  • anonymous
The following function represents the profit P(n), in dollars, that a concert promoter makes by selling tickets for n dollars each: P(n) = -250n^2 + 2,500n - 5,250 Part A: What are the zeroes of the above function, and what do they represent? Show your work.
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
@SolomonZelman
SolomonZelman
  • SolomonZelman
What does n represent?
anonymous
  • anonymous
dollars

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More answers

SolomonZelman
  • SolomonZelman
precisely, n, is a price per ticket.
SolomonZelman
  • SolomonZelman
What does P(n) represent?
anonymous
  • anonymous
profit
SolomonZelman
  • SolomonZelman
Yes, when P(n) is 0, that means that the profit is zero (i.e. made nothing), right?
anonymous
  • anonymous
yes
SolomonZelman
  • SolomonZelman
The x-intercepts of this function are the values of n (or the value of the price per ticket) with which the P(n) (or the profit) is 0. (There are going to be 2 x-intercepts)
anonymous
  • anonymous
okay
SolomonZelman
  • SolomonZelman
So, if you find the x-intercepts, you are going to find the 2 possible values of a price per ticket with which the promoter will NOT profit (but will not lose).
SolomonZelman
  • SolomonZelman
So, do you see what these x-intercepts would mean?
anonymous
  • anonymous
yes
SolomonZelman
  • SolomonZelman
Ok, now you have to solve for these x-intercepts.
anonymous
  • anonymous
the x intercepts are 3 and 7?
SolomonZelman
  • SolomonZelman
yes, very good!
SolomonZelman
  • SolomonZelman
Perfect!
SolomonZelman
  • SolomonZelman
So, when the ticket costs 3$ or 7$ , then the promoter doesn't gain or lose.
anonymous
  • anonymous
now what?
SolomonZelman
  • SolomonZelman
when the *average* ticket I should say
SolomonZelman
  • SolomonZelman
Well, all you had to do is to find these zero (these x-intercepts), and to then say what these x-intercepts represent in your situtation.
SolomonZelman
  • SolomonZelman
you found x=3, and x=7 ((( and that is correct ))) now you have to say what do these intercepts mean/do/represent?
SolomonZelman
  • SolomonZelman
just say what we have agreed on in the beginning.
anonymous
  • anonymous
can you help me with part B?
SolomonZelman
  • SolomonZelman
what is part B?
SolomonZelman
  • SolomonZelman
I can try my best with it:)
anonymous
  • anonymous
Part B: Find the maximum profit by completing the square of the function P(n). Show the steps of your work.
SolomonZelman
  • SolomonZelman
Oh, good
SolomonZelman
  • SolomonZelman
``` SIDE - NOTE: Most people would say that this question requires calculus, but in a case of a parabola (a quadratic does not). (this what most people say is a mistake). ``` ALL YOU GOT TO DO: You have to write your P(n) in a vertex form, and the vertex is going to be the maximum.
anonymous
  • anonymous
so (5,1000)?
SolomonZelman
  • SolomonZelman
Let me see.... i wil be typing, and if it is right I will post the work, and if it is not, then I will ask you to redo it and follow along with me.
SolomonZelman
  • SolomonZelman
hope that is fair.
anonymous
  • anonymous
yes
SolomonZelman
  • SolomonZelman
\(\large\color{black}{ \displaystyle P(n) = -250{\rm n}^2 + 2,500{\rm n} - 5,250 }\) \(\large\color{black}{ \displaystyle P(n) = -250({\rm n}^2 -10{\rm n}) - 5,250 }\) \(\large\color{black}{ \displaystyle P(n) = -250({\rm n}^2 -10{\rm n}+25-25) - 5,250 }\) \(\large\color{black}{ \displaystyle P(n) = -250({\rm n}^2 -10{\rm n}+25)+(-250)(-25) - 5,250 }\) \(\large\color{black}{ \displaystyle P(n) = -250({\rm n}^2 -10{\rm n}+25)+1000 }\) \(\large\color{black}{ \displaystyle P(n) = -250({\rm n}-5)^2+1000 }\)
SolomonZelman
  • SolomonZelman
yes, that is correct
SolomonZelman
  • SolomonZelman
And quite quick
anonymous
  • anonymous
1 graphed it
SolomonZelman
  • SolomonZelman
oh, you graphed it... good, but it is very good (I would insist that even required) to know that without graphing.... in any case though, lets do a little review of what you have actually found just now,
anonymous
  • anonymous
the axis of symmetry would be 5 right? (Thats part C)
anonymous
  • anonymous
okay
SolomonZelman
  • SolomonZelman
yes part C is correct
SolomonZelman
  • SolomonZelman
now the review of what does the vertex of (5,1000) actually mean in this case.
anonymous
  • anonymous
thats the maximum about of profit the promoter can make?
SolomonZelman
  • SolomonZelman
that is you are refering to the point to a 5 or a 1000 ?
anonymous
  • anonymous
1000 makes more sense 1 think
SolomonZelman
  • SolomonZelman
yes
SolomonZelman
  • SolomonZelman
and what does 5 mean, can you tell me?
anonymous
  • anonymous
the amount the tickets cost?
SolomonZelman
  • SolomonZelman
yes
SolomonZelman
  • SolomonZelman
So when the average ticket costs 5$, you get a maximum profit of 1000
anonymous
  • anonymous
makes sense
SolomonZelman
  • SolomonZelman
A quite small, if not miserable profit in a real life situation... but won't be talking about a real life situation because such situations are never modeled with quadratics in real life....
SolomonZelman
  • SolomonZelman
yeah, so you got any questions regarding any of the PARTS ?
anonymous
  • anonymous
nope thats it
anonymous
  • anonymous
as usual you're the most helpful person on the whole site. Thanks!
SolomonZelman
  • SolomonZelman
\(\large{\bbox[5pt, cyan ,border:2px solid black ]{ \rm Thanks! }}\)
SolomonZelman
  • SolomonZelman
I wouldn't say I am most helpful, but won't deny some use.; you are always welcome!

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