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Yopenmain Home My Classes User Settings| Log Out ourse Forums Calendar Gradebook Home MA 1852 Calculus for Business Spring 2021 Assessment2.9 Score: 3.6/14 4/14 ans...

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Yopenmain Home My Classes User Settings| Log Out ourse Forums Calendar Gradebook Home MA 1852 Calculus for Business Spring 2021 Assessment2.9 Score: 3.6/14 4/14 answeredQuestionbaseball team plays in a stadium that holds 56000 spectators_ With the ticket price at 512 the average attendance has been 24000 When the price dropped to 511 the average attendance rose to 28000 Assume that attendance linearly related to ticket priceWhat ticket price would maximize revenue?Question Help:ViceoSubmit Quest

yopenmain Home My Classes User Settings| Log Out ourse Forums Calendar Gradebook Home MA 1852 Calculus for Business Spring 2021 Assessment 2.9 Score: 3.6/14 4/14 answered Question baseball team plays in a stadium that holds 56000 spectators_ With the ticket price at 512 the average attendance has been 24000 When the price dropped to 511 the average attendance rose to 28000 Assume that attendance linearly related to ticket price What ticket price would maximize revenue? Question Help: Viceo Submit Question



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Stadium Revenue A baseball team plays in a stadium that holds $55,000$ spectators. With the ticket price at $\$ 10,$ the average attendance at recent games has been $27,000$ . A market survey indicates that for every dollar the ticket price is lowered, attendance increases by $3000.$
(a) Find a function that models the revenue in terms of ticket price.
(b) Find the price that maximizes revenue from ticket sales.
(c) What ticket price is so high that no revenue is generated?

The question they're asking to show that all the ISIS and a struggle with a given pedometer. First The one with the greatest area is equilateral. So here, thanks Industry, go those sides with value S. Is equal and the other side is B. And the height of the triangle is each so S squared is equal to a squared plus B squared by four. Therefore eight squared is equal to a square minus B squared by four. The radio. Okay, something is equal to half B. Route under a square minus B squared by four. Not let the parameter Vp. Mhm. Yeah. So yeah to S plus B. Yeah is equal to P or as equal to P minus B by two. Therefore A of B is equal to have bill into root. Under B minus B. Hole squared divided by four minus B squared by four. What? Mhm. Mhm. This is equal to be into root under Peace Square -2. PB by four. The almost and here a dashed b is equal to root. Underpay square minus two. P. B divided by four minus Bp by four. Divided by route under P square minus to BB is equal to minus three. P B plus p square. All divided by four into root. Under peace. Square minus to BB. Yeah, a lot of questions. Therefore, yeah a dash B is equal to zero. This means minus three. P B plus b. Square is equal to zero. Or B is equal to P by three. Now, since a dashed B is greater than zero four B is less than p by three and a dash B is less than zero for B is greater than P by three. The Yeah, there is an absolute maximum. Yeah. Have a couple of things yourself. When B is equal to P by tree. I want to help. Yeah. Right. Coming up working with the money. Yeah. Mhm. But then to S plus B by three is equal to P. What's that? So S. is equal to p by three and therefore S is equal to be this contract? Yeah. Yeah. All right. And since the site is equal to side B, therefore triangle is equal lateral. Yeah. Yeah. Yeah. Thank you. Hence this is the required answer. Mhm. Thank you of the given question.

Hey, guys. So right now we're gonna be taking a look at question number 74 in your textbook, and that is asking us to help maximize the revenue that a company makes when it changes its ticket prices. So our revenue is going to be equal to our price. Times are quantity. So that's just kind of for every ticket that they sell, how much money they make. And this is just our revenue, which is again, just how much money they make. So we're trying to figure out when our price and our quantity are gonna be at the perfect place to make the absolute most money. So first we need to take a look at their past prices and quantities. So when tickets were $11 they sold 26,000 tickets, and then when they're priced was $9 a ticket, they sold 31,000 tickets, so that's a little bit of a difference there. But then we have to figure out exactly how much that difference was. So we're gonna take our original quantity and we're going to subtract our new quantity, and then we're going to take our new pry our old price and subtract our new price. So 26,000 minus 31,000 gives us negative 5000 and then 11 minus nine gives us two, and then when we divide negative 5000 by two, we get negative 2500. So this right here is going to be how much they lose, how many tickets they lose every time their price goes up a dollar. All right, so now that we have this, we need to put this into an equation that we can work with. So our quantity is going to be the same thing as how much they lose per dollar, that it goes down, which is gonna be a price. But then this isn't quite enough. We need to figure out where they started from. So we're gonna be looking for a be here, too. So the first thing we're gonna want to do is we're gonna want to pick some of our ticket prices, and our quantity is to plug into R P and R. Q. So I'm gonna go ahead and choose our newest ticket price. We've got 31,000 tickets sold, equals 2500 dollars, lost at $9 a ticket, and then we're trying to figure out our be. So we've got 31,000 is the same as $9 times 2500 which is gonna give us negative 22 1005 100 plus our B. So the first thing we don't want to do is to get our B by itself. So we're gonna add this to both sides, and we're gonna end up with 5 53,000 500 and that's going to be our be here. Okay, so now we can go ahead and writes this actual equation appears we've got our quantity is the same thing as our negative 2500 p plus our 53,500. So now that we have this, we're going to go ahead and plug this Q into our into our revenue, Um, equation up here. So this right here is gonna be equal to our cue in this equation. So we're gonna plug that in, but negative 2500 p plus our 53,500. And so now that we have this, we're gonna go ahead and distribute. It's we've got negative 2500 p squared, plus 53,500 p. So this is now just a normal parable. Equations, We've got it, and it's got a negative coefficient. So that means it's gonna open down like this. We're trying to find our maximum revenue, which is gonna be right here. And so the way we're gonna figure this out is we're gonna plug this into our access of symmetry because that access of symmetry is gonna give us the X value, which is what we're looking for. This pee right here because that's the price in which they'll make the most money. So let's go ahead and plug it into our negative be over two A. So we've got our negative B, which is our 53,500 all over. Our two times are a which is that negative 2500. So if we go ahead and cancel out these positives and I like to just go ahead and get rid of both of these ahh double zeros at the end of that because it's pretty much just dividing by 100 but it just makes everything simpler. So when you go ahead and multiplied by the two and then divide by the whole thing. You end up getting 10.7, and this right here is going to be the ticket price that will end up making this company the most money possible.

Okay, so this problem gives us a couple of points, if you will. Um, it says the maximum number of Spectators in a soccer stadium that 62,000 it tells us for $11. Call it my ex value. The number of people is 26,000. Okay. And then, uh, the price of dropped to $9. With the price dropping, we got more people. It went up to 31,000 and says his assuming that this is linear, what would be the ticket price that would fill it up so would give us 62,000. So let's first come up with an equation for these 1st 2 points. Um, my slope, Um, it's just my change in X ever changing line. Says it's a So why is going up as X is going down? So it's gonna be a negative slow. And then my wife changed by a factor of 5000 and my exchange by a factor of two. Okay, so my slope is negative 2500. So I have Why equals negative 2500 times acts plus my wife intercept, which is what it would be like when x zero. Um so I can just plug in one of these values. Uh, so putting it in. If I played in 9000 I have to get 31,000 s o. That extra piece is going to be 53,500. Okay, so that will make sure that when I plug in nine, I get 31,000 went up, like in 11. I will get 26,000 s. So now I need to solve. For when is that gonna equal 62,000. So credits clients. I got 62,000 negative. 2500 acts plus 53,500. So if I subtract 53,500 from both sides, that's gonna give me 8500 is equal to negative. 2500 axe. They had a band. Both sides by negative 2500. I'll have eggs is negative. $3.40 which means to fill up the stadium, you're gonna have to pay each person $3.40 to come to the game. So maybe a linear model isn't the best for this. Um, and it kind of makes sense if we go back to gain 5000 people. We had to drop it by $2 But we have to gain another 30,000 people. So we have to drop it by another $12 to get 30,000 people, which is gonna put us into the red so this stadium will not get fullness. We increase some other way. Way to get people to come. Maybe have a winning team. Okay, well, thank you very much.

All right. So we're at a baseball stadium where the average president ticketus $15. And at that price, the average attendance is 20,000 people. The attendance goes down by 400 people for every $1 increase in ticket price. So were first asked to model the revenue as a fun Excuse me, The number of Spectators is a function of to get price. So are Spectators start at 20,000 and they decrease by 400 people for every $1 increase in price. So in orderto show are $1 increase in price. X is gonna be our ticket price minus the average price of 15 which gets us to 20,000 people. So this expression here will tell us how many dollars we actually increased by times that by 400 subtracted from 20,000 will tell us the number of Spectators for part B, we want to know revenue. Well, our revenue function is gonna be our Our attendance times are ticket price, which is X should define that X is our to get price. So, um, our attendance is modeled just with this equation here. So we're gonna simplify our equation from part a 20,000 minus 400 times X minus 15. We need to get rid of these parentheses and combine like terms before we continue. So 20,000 minus 400 X. Um, plus 400 times 15. 6000. All right, Now, combining like terms, 20,000 plus 6000 is 26,000 minus 400 X. Now that's our attendance. Now we need to multiply this quantity by X are a number of people times X since X is the cost of the ticket that tells us how much revenue we make. So we have to use the distributive property again. Extremes 26,000 is 26,000 x minus X times 400 X is negative. 400 X squared. Now, to finish this off, I'm gonna rewrite this, um, in standard notation, which means rewriting it such that are higher variable or are higher degree term miss first so negative 400 x squared plus 26,000 X. It's not a k. That's not what we want. And this function right years, the function for revenue. So part a large number of Spectators, Part B is our revenue. Given that question,


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