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(9 poinis)The psychology club is having self-proclaimed demonstrate his abilities. He charges 5130 psychic come to their campus fund-raising event to chance to have...

Question

(9 poinis)The psychology club is having self-proclaimed demonstrate his abilities. He charges 5130 psychic come to their campus fund-raising event to chance to have the psychic for these events, and the club is read the ticket holders mind. Let x e charging $2.5 for tickets with represent money in a linear model which repre sent the number of tickets sold and based can be used to estimate Iie profit _ upon the number of tickets sold. (positive) or loss (negative) How much would the club gain or

(9 poinis) The psychology club is having self-proclaimed demonstrate his abilities. He charges 5130 psychic come to their campus fund-raising event to chance to have the psychic for these events, and the club is read the ticket holders mind. Let x e charging $2.5 for tickets with represent money in a linear model which repre sent the number of tickets sold and based can be used to estimate Iie profit _ upon the number of tickets sold. (positive) or loss (negative) How much would the club gain or lose by selling 14 tickets? (Exress vour answer rounded correclly to Ihe nearest. ansWCI there centl Be sure lossl) Include mnus sign with your dollars many tickets must be sold In order for the club to break even? Express your answer rounded up to the next whole (lcket ) lickets How many (ickets must be sold In order for Ihe club (o make prolit 0f 55302 (Express your answer rounded up to the next whole (icket ) tickets If you haven"( answered the quesiion correctly aitempts you can get hint



Answers

Tickets for a particular flight are $\$ 250$ apiece. The plane seats 120 passengers, but the airline will knowingly overbook (i.e., sell more than 120 tickets), because not every paid passenger shows up. Let $t$ denote the number of tickets the airline sells for this flight, and assume the number of passengers that actually show up for the flight, $X,$ follows a $\operatorname{Bin}(t, 85)$ distribution. Let $B=$ the number of paid passengers who show up at the airport but are denied a seat on the plane, so $B=X-120$ if $X>120$ and $B=0$ otherwise. If the airline must compensate these passengers with $\$ 500$ apiece, then the profit the airline makes on this flight is $250 t-500 B$ . (Notice $t$ is fixed, but $B$ is random.)
(a) Write a program to simulate this scenario. Specifically, your program should take in $t$ as an input and return many values of the profit variable $250 t-500 B .$
(b) The airline wishes to determine the optimal value of $t$ , i.e., the number of tickets to sell that will maximize their expected profit. Run your program for $t=140,141, \ldots, 150,$ and record the average profit from many runs under each of these settings. What value of $t$ appears to return the largest value? [Note: If a clear winner does not emerge, you might need to increase the number of runs for each $t$ value! $]$

In the first part. According to Given, uh, Matrix A is equal to nine 11 tartine 15 16 It seven for the X is equal to X. Why is that? And Matrix B is equal to 7 40 100 for and it 28 in the second bar. Yeah, Multiplying by X is equal to be form is nine 11 it 13 15 16 Good seven for the multiplied by X. Why is that? He wants to 7 40 104 828 in the third bar it in Worse is calculated as apply are one is equal to I wouldn't be worked by night are you? Is he going to do are U minus 13 at one. Our do is equal to minus nine divided by eight Are you now? I won. Bless are three on matrix A. We will get hey in worse is equal to seven divided by four minus seven divided by four one minus 27 Divided by 28 can be one divided by 28 Minus life The white by seven minus 2091 by 56 25 divided wife of 36 minus one divided by seven Also X Why and then is equal to hey in worse 7 40 do 100 for he tender Got the No X is equal Do dollar 16 Why is he so dollar going? The eight is a or do no wonder 36 in part b using man drinks right? One I mean to three. Yeah. Monte Frank by excellent. Why one said one it wants to do for the level Yeah, X one is equal to minus seven. And why does is they want to seven here, X, God be negative So there is no such combination.

In this problem, we are given a lot of information about a saleswoman, and the different amounts of cell phones is she sells. Ah, and the commission that she makes for each week. So for every problem, access to a Let X, Y and Z represent the Commission on Standard Deluxe and Super Deluxe cell phones, and we want to write these right this information as a system of equations. Also, we know that the standard is going to correspond to X deluxe model, correspond to why and Super Deluxe will correspond to Z. So essentially each of our weeks is going to correspond to one of our equations in our system. I'm so for a week when we know that we have nine standards. So nine x plus 11 times our deluxe, which will make 11. Why plus eight times are Super Deluxe and this is going to give us $740 on me too. We're going to sell 12 standard models a 12 X plus 15 deluxe wife plus 16 Super Deluxe Easy, which is going to give us $1204. And finally, on our third week, we have three standard models of three X plus 70 look +71 plus 14 Super Deluxe See is going to be equal to $828. I'm so that's part a big problem for a party over problem. We want to write this system of equations as a matrix equation. I'm so essentially we're just going to be able to write this actually do that on the top of here as a co efficient matrix, which we know I's going to be. In our first equation, we have nine 11 eight. Our second equation has coefficients of 12 15 and 16 and our third equation as coefficients 37 and 14. And we're multiplying this by are variable matrix, which is X y Z, and this will be equal to the constants on the right hand side of the equation so equal to 740 1204 and 828 and finally, for party ever problem. We want to find the inverse of the co efficient matrix A and use it to solve the matrix equation in part beat. I'm so once we do that, it's going to answer the question How much commission does the sales saleswoman earn on each model of cell phone? I'm so we could go ahead and start working on finding our universe of our matrix here. Um, I'll go ahead and give us some extra space to work as we know that we're going to write this out, um, as a three by six matrix, where the left three by three Matrix is going to be our original matrix that were given 37 14 and then on the right inside, we're going to draw dash line and then write our identity matrix out. And so, essentially, all we're going to dio is ro reduce so that the left hand side of our equation is going to give us, uh, I knew I did in the Matrix. Um, so right away, we can see that, Uh, regardless of what we do, this is going to give us quite a few fractions here, and so I'm going to go ahead and begin by dividing my entire first road. Uh, fine, actually. Always And start with our third row, we can go ahead and compute row two minus four times our third row and row one finds three times or third route. And so, essentially, the reason that I chose to do this, um, was because I know it's going to give us some zeroes in our position there. Um, so our top row row one minus three, row three. Now we get nine minus nine, which is zero 11 minus three times seven. So I love in my eyes. 21 will give us negative 10 and then we have eight minus 14 Times Street. Um and so when we will buy that out, it's a tract that's going to leave us with negative 34. Well, then we have 10 negative. Three, our second row. We have ro to minus four times row three. So we have 12 minus 12 which is zero of 15 minus four times seven. Eso 15 minus 28 is going to be negative. 13 on. Then we have 16 minus four times 14 which is going to give us negative 40. And then we have 01 negative three and our third row is going to see is him 37 14 001 And from here we can see that we now have nothing that's going to cancel really nicely. Um, so I'm going to go ahead and start by dividing my top equation by 10 or my top row by Ted. So, row one over 10 this is going or negative time. This will give us 01 3.4 and then 0.10 negative 0.3. Our second row is still zero negative. 13 negative. 40 01 negative three. And her third row is 3 7/14 001 But actually, I'll go ahead and divide this. Divide everything by three here to change this, to be in the form that we want our equation to be in or our identity matrix to be in so again, dividing everything by 33 over three will give us one. I'm just going to leave this as 7/3 and 14 3rd and then we have 00 1/3. So from here, we can see that in order to get rid of the negative 13 in Row two, we're going to want to add a 13 row one to get to there. I'm so we'll go ahead and I'll actually replace our performer. Rose Swap on rose one and three so no one is not going to be one 7/3. 14 3rd 00 1/3 um, And Row three is not going to be 01 3.4 a negative 0.1 zero. Ah, and 0.3. And row two, we are going to be subtracting a 13 of our original row one from I'm so we get 00 a negative force yet? Negative. 40 minus 13 times 3.4 is going to give us negative. 84.2 Ah, in our next position. Now we have zero minus a 13 times 130.1. So that'll be negative. 1.3 ah one minus zero and negative three minus or should be plus, actually a negative three plus a 0.3 times 13. Essentially. Ah, that's just the same thing as three times a point. Three times 13 minus three actually. Give us negative 11.7. Um, And in our first position right here, I realize that I accidentally subtracted, but I should have actually added so that should have been negative. 40 plus 13 times, 3.4, which would actually be 4.2, huh? Um and so from here, we can go ahead and perform somewhere. Rose Wops. I'm going to go ahead and swap rose two and three here, huh? But And so instead of continuing Thio more finds out, I'll go ahead and just get to the end here because it's going to take quite a bit of time. But once we end up finishing this role reduction, we're going to be left with are inverse matrix as seven over four. Negative seven over four one in her first wrote our second rule being negative. 27 over 28. 31. Number 28. And then finally negative. Five over seven. And our third row will be negative. 29 over 56 25 over 56. Negative, one over seven. And so from here, now that we have are inverse matrix. We know that we're just going to multiply this by our matrix that we found, um, or are a constant matrix, which started with 740 from our first week 1204 from our second week and 828 from our third week. And once you go to buy these together, we find that are a standard model is going to give us $16 in commission. The deluxe model will be $28 and the Super Deluxe model is $36 in commission.

So on Tuesday. Ninth, a local restaurant has a past a special, and I really like the restaurants pasta and his willingness to pay for each serving is shown in the table. As you can see on the first question is, if the price off seven um, pasta is $4 how many servings will vary by and how much consumer surplus does he receive? So I we can buy 4/7 off from for four sevens of pasta because consumer will bypass tha. If it's our willingness to pay for the past side either greater than or equal to the price of pasta. So are we well, by for servants off pasta and now the consumer support, on the other hand, is some of the difference between the willingness to pay and the price of pasta. So for this question, the consumer surplus, because to $10 minus for the last at the price plus $8 minus $4 pause $6 minus $4 and this is from the table, plus $4 miles $4 so because of my surplus, then be hosted $12. All right, so moving onto the second question the following week are is back at the restaurant, the game, but now the price of its seven is now $6. How much does it stop because my supplies decrease compared to the previous week? So now that is, um, price. Divisive Pasta is $6. I will now by three sevens of pasta on because most supposed to be closed to $10 which is a price minus $6. That is the current price. Klaus $8 minus $6 plus $6 minus $6 on because my supplies to be house $6. So now, as a result of condiments, a plus falls from $12 which was before, to $6 on that's 50% approximately. So that's the answer for that. Now we're gonna answer the tall question. One week later, it goes to the restaurant again on it discovers that the restaurant is offering and all you can eat special for $25. So you eat all you can eat for $25. Now how much passed out we eat and how much because my supplies does he receive now? So it doesn't all you can eat special and the price the Ari go on pace for seven is going to be zero because you're eating all you can eat. So twice past seven, we host 20 on. Therefore, you'll be able to eat six servings of pasta on the 2000 month is willing to pay for this. Six servings is gonna be $60 so right attested Ullas. It would eat 67 off pasta. Andi, the amount the total amount is willing to pay for six seven will be cost to $30. So this is the sum of amounts is willing to pay for each individual seventh. So the actual pay, um, it's $25. As you can see, all you can insist $25 So the actual pay is $25. Is willingness to pay is $30 which is right here he started. S so therefore the consumer supposed to be the difference between the less to pay and the actual pay, and that will be $30 minus $25. So consumer surplus easy. Close to $5. Now the final question Suppose that you own the restaurant and I read the typical customer. What is the X prize? You can charge for all you can eat on the special and still attract more customers. So if you own the restaurant and I read the typical customer, which means it comes every time what the X prize you can charge for the all you can eat and still attract customers. So in this case, off 37 there are you be able to consume six servings, as you can see and give him a surplus off $30 which there are questions said so R e Kahn consume six servants on Kazuma. Surplus is equals to $30. So if I read a special customer, this is gonna be the ice price you can charge for. You can charge for the special. So if Ari is a special Costilla Yukon charge $30 as the ice price, so for the special, So that's the answer. Is that question

Okay, so in this question we have to form some equations into variable and then we have to solve them by elimination method. Okay, so the first part is about to find a fraction value. Okay, so we have to find a fraction value, let's say the numerator is X. And the denominator is why? So we just have to find the value of X and Y. For that we have we are given some conditions. The first condition is if we add one to the numerator and we subtract one from the denominator, the fraction becomes one, that is X plus one equals two by minus one. So we get by minus X equals true too. This is our first condition similarly for the second condition, we are given that if we add one to the denominator Then the equation becomes, then the fraction becomes one x 2. So that equation on simplifying will be the works equals two, Y plus one. This is our second equation. So the two equations, which we get is y minus X equals to two and two X minus Y equals to one. We can see that on adding these equations we can eliminate white. So we will add these two equations will get X equals 2. 3. Okay. And on solving we get vie equals two. Right? So this is the answer of first part. Moving on to the 2nd part. Moving on to the 2nd part. We are given That five years ago. No ribose three as old as so. No. So it's all about finding the age. Let's just say that Nordea's edge is X. And so knows age is right. Yeah. Okay. We are given that five years ago. That means we have to subtract five from both ages. Okay. Five years ago Nouri's age was three times the sun whose age unseen cliff eyeing this, we get three y minus X equals two. then. Okay this is our equation. 1st. For second equation we are given That 10 years later That is we have to add 10 to both the ages. 10 years later Nori's age becomes double. The sun was age solving this? We get X -2 Y equals that. So this is a second equation solving this two equations. By elimination method. We can just add these two equations to eliminate X. Okay, adding these two equations, we get Y two b. 20 and extremely 50. That is so news ages 20 and Nouri's ages 50. Okay so let's let's move To the 3rd part. Okay. For the 3rd part we are given that the sum of a to desert number is nine. Let's say the two dessert number is 10 X plus Y. Who does that number are of the form 10 x plus y. So we are given some of the desert. The desert are exceeded by. The sum of the desert is given to be nine. So this is simple and fast equation. Then we are given that if we revolves the number, The nine times of this number is two times the rivers of tell a force number. Okay, simplifying this equation, we get eight x equals to white. That is eight X minus Y equals to zero. This is our second equation to eliminate why. We can just add these two equations. Okay adding these two equations, we get nine x equals to nine. That is x equals to one And the value of Y will become eight. We have to find the number. The number would be 10 X. Less. Why? That is 18. The number will be 18. Okay, So moving on to the 4th part. For the 4th part, We are given that Mina went to a bank to withdraw some $22,000. Okay? And she has to take only 50 and ₹100 notes. Let's say the ₹50 notes. ₹50 notes are ex she have X ₹50 notes and ₹100 notes are right. Okay. She says that she have 25 notes in total. That is the total notes are 25 and the total money. The situation is first equation and the total money adds up to 2000 bucks. So total money would be 50 X plus 100 100 Y. Giving us to be 2000 solving this equation. Simplifying the equation will get X plus two Y equals to 40. This is our second equation. We can just subtract these two equations to eliminate X expressed away equals to 40 and X plus Y equals to 25. Subtracting these two equations, we get Y to be 15 And X. two written that does she have 10 notes of ₹50.15 notes of ₹100. Okay, Moving on to the last part, that is 5th part, 5th part. He says that a lending library has a fixed charge for the first three days, let's say the fixed charge for the first three days if X. And it says it has additional charge for the remaining these. So let's say the additional charge 40 is right. Okay. She says if she has borrowed it for 27 days, sorry, It says if she had borrowed 84 seven days, that is X. Is the fixed charge for three days. The remaining additional day will be four days, Okay? And the charge is ₹27. Similarly, for five days she has to pay ₹21 for five days additional devil bit, two days. ₹21 simply subtracting these two equations. We get to Y equals to six. That is why equals 23 And X. It was 2 15. So the fixed charges are $15, and the additional charge per day will be $3. Thank you.


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