Breakeven Point
$begingroup$
To examine the effectiveness of its four annual advertising promotions, a mail order company has sent a questionnaire to each of its customers, asking how many of the previous year's promotions prompted orders that would not have otherwise been made. The accompanying table lists the probabilities that were derived from the questionnaire, where X is the random variable representing the number of promotions that prompted orders. If we assume that overall customer behavior next year will be the same as last year, what is the expected number of promotions that each customer will take advantage of next year by ordering goods that otherwise would not be purchased?
X: 0 1 2 3 4
P(X) 0.078 0.242 0.337 0.16 0.183
A previous analysis of historical records found that the mean value of orders for promotional goods is 29 dollars, with the company earning a gross profit of 29% on each order. Calculate the expected value of the profit contribution next year. Answer is 17.89648
The fixed cost of conducting the four promotions is estimated to be 20000 dollars with a variable cost of 4 dollars per customer for mailing and handling costs. What is the minimum number of customers required by the company in order to cover the cost of promotions? (Round your answer to the next highest integer.)
Breakeven point:?????
I have tried to do 20000 = (# of customers) (29-4)
But got it wrong.... I don't know what method to use to find the breakeven point.
Thank you!
statistics
$endgroup$
add a comment |
$begingroup$
To examine the effectiveness of its four annual advertising promotions, a mail order company has sent a questionnaire to each of its customers, asking how many of the previous year's promotions prompted orders that would not have otherwise been made. The accompanying table lists the probabilities that were derived from the questionnaire, where X is the random variable representing the number of promotions that prompted orders. If we assume that overall customer behavior next year will be the same as last year, what is the expected number of promotions that each customer will take advantage of next year by ordering goods that otherwise would not be purchased?
X: 0 1 2 3 4
P(X) 0.078 0.242 0.337 0.16 0.183
A previous analysis of historical records found that the mean value of orders for promotional goods is 29 dollars, with the company earning a gross profit of 29% on each order. Calculate the expected value of the profit contribution next year. Answer is 17.89648
The fixed cost of conducting the four promotions is estimated to be 20000 dollars with a variable cost of 4 dollars per customer for mailing and handling costs. What is the minimum number of customers required by the company in order to cover the cost of promotions? (Round your answer to the next highest integer.)
Breakeven point:?????
I have tried to do 20000 = (# of customers) (29-4)
But got it wrong.... I don't know what method to use to find the breakeven point.
Thank you!
statistics
$endgroup$
add a comment |
$begingroup$
To examine the effectiveness of its four annual advertising promotions, a mail order company has sent a questionnaire to each of its customers, asking how many of the previous year's promotions prompted orders that would not have otherwise been made. The accompanying table lists the probabilities that were derived from the questionnaire, where X is the random variable representing the number of promotions that prompted orders. If we assume that overall customer behavior next year will be the same as last year, what is the expected number of promotions that each customer will take advantage of next year by ordering goods that otherwise would not be purchased?
X: 0 1 2 3 4
P(X) 0.078 0.242 0.337 0.16 0.183
A previous analysis of historical records found that the mean value of orders for promotional goods is 29 dollars, with the company earning a gross profit of 29% on each order. Calculate the expected value of the profit contribution next year. Answer is 17.89648
The fixed cost of conducting the four promotions is estimated to be 20000 dollars with a variable cost of 4 dollars per customer for mailing and handling costs. What is the minimum number of customers required by the company in order to cover the cost of promotions? (Round your answer to the next highest integer.)
Breakeven point:?????
I have tried to do 20000 = (# of customers) (29-4)
But got it wrong.... I don't know what method to use to find the breakeven point.
Thank you!
statistics
$endgroup$
To examine the effectiveness of its four annual advertising promotions, a mail order company has sent a questionnaire to each of its customers, asking how many of the previous year's promotions prompted orders that would not have otherwise been made. The accompanying table lists the probabilities that were derived from the questionnaire, where X is the random variable representing the number of promotions that prompted orders. If we assume that overall customer behavior next year will be the same as last year, what is the expected number of promotions that each customer will take advantage of next year by ordering goods that otherwise would not be purchased?
X: 0 1 2 3 4
P(X) 0.078 0.242 0.337 0.16 0.183
A previous analysis of historical records found that the mean value of orders for promotional goods is 29 dollars, with the company earning a gross profit of 29% on each order. Calculate the expected value of the profit contribution next year. Answer is 17.89648
The fixed cost of conducting the four promotions is estimated to be 20000 dollars with a variable cost of 4 dollars per customer for mailing and handling costs. What is the minimum number of customers required by the company in order to cover the cost of promotions? (Round your answer to the next highest integer.)
Breakeven point:?????
I have tried to do 20000 = (# of customers) (29-4)
But got it wrong.... I don't know what method to use to find the breakeven point.
Thank you!
statistics
statistics
asked Oct 14 '17 at 23:12
Gill DaveGill Dave
176
176
add a comment |
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
In somewhat improved notation, the PDF table for the random variable $X$ is
k: 0 1 2 3 4
P(X=k): 0.078 0.242 0.337 0.160 0.183
First, notice that $sum_{k=0}^4 P(X=k) = 1,$ as required for a PDF. Then $$E(X) = sum_{k=0}^4 kP(X = k) = 2.128.$$
The profit per order is $29(.29) = $8.41.$ So the profit on the expected $2.128$ orders per customer
is $$17.89648.$
The profit for $n$ customers is $$17.89648n.$ From what you say, I suppose the cost of a campaign reaching $n$ customers
to be $$(20,000 + 4n).$ I will leave it to you to find the number $n$ of
customers to break even, as required.
$endgroup$
$begingroup$
Stupid question... but would I plug it in as: (20,000+4n)=17.89648?
$endgroup$
– Gill Dave
Oct 15 '17 at 4:46
$begingroup$
Almost that. Look again.
$endgroup$
– BruceET
Oct 15 '17 at 6:27
1
$begingroup$
Oh my goodness, thank you so much!
$endgroup$
– Gill Dave
Oct 15 '17 at 14:30
add a comment |
Your Answer
StackExchange.ifUsing("editor", function () {
return StackExchange.using("mathjaxEditing", function () {
StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix) {
StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["$", "$"], ["\\(","\\)"]]);
});
});
}, "mathjax-editing");
StackExchange.ready(function() {
var channelOptions = {
tags: "".split(" "),
id: "69"
};
initTagRenderer("".split(" "), "".split(" "), channelOptions);
StackExchange.using("externalEditor", function() {
// Have to fire editor after snippets, if snippets enabled
if (StackExchange.settings.snippets.snippetsEnabled) {
StackExchange.using("snippets", function() {
createEditor();
});
}
else {
createEditor();
}
});
function createEditor() {
StackExchange.prepareEditor({
heartbeatType: 'answer',
autoActivateHeartbeat: false,
convertImagesToLinks: true,
noModals: true,
showLowRepImageUploadWarning: true,
reputationToPostImages: 10,
bindNavPrevention: true,
postfix: "",
imageUploader: {
brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
allowUrls: true
},
noCode: true, onDemand: true,
discardSelector: ".discard-answer"
,immediatelyShowMarkdownHelp:true
});
}
});
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f2472654%2fbreakeven-point%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
In somewhat improved notation, the PDF table for the random variable $X$ is
k: 0 1 2 3 4
P(X=k): 0.078 0.242 0.337 0.160 0.183
First, notice that $sum_{k=0}^4 P(X=k) = 1,$ as required for a PDF. Then $$E(X) = sum_{k=0}^4 kP(X = k) = 2.128.$$
The profit per order is $29(.29) = $8.41.$ So the profit on the expected $2.128$ orders per customer
is $$17.89648.$
The profit for $n$ customers is $$17.89648n.$ From what you say, I suppose the cost of a campaign reaching $n$ customers
to be $$(20,000 + 4n).$ I will leave it to you to find the number $n$ of
customers to break even, as required.
$endgroup$
$begingroup$
Stupid question... but would I plug it in as: (20,000+4n)=17.89648?
$endgroup$
– Gill Dave
Oct 15 '17 at 4:46
$begingroup$
Almost that. Look again.
$endgroup$
– BruceET
Oct 15 '17 at 6:27
1
$begingroup$
Oh my goodness, thank you so much!
$endgroup$
– Gill Dave
Oct 15 '17 at 14:30
add a comment |
$begingroup$
In somewhat improved notation, the PDF table for the random variable $X$ is
k: 0 1 2 3 4
P(X=k): 0.078 0.242 0.337 0.160 0.183
First, notice that $sum_{k=0}^4 P(X=k) = 1,$ as required for a PDF. Then $$E(X) = sum_{k=0}^4 kP(X = k) = 2.128.$$
The profit per order is $29(.29) = $8.41.$ So the profit on the expected $2.128$ orders per customer
is $$17.89648.$
The profit for $n$ customers is $$17.89648n.$ From what you say, I suppose the cost of a campaign reaching $n$ customers
to be $$(20,000 + 4n).$ I will leave it to you to find the number $n$ of
customers to break even, as required.
$endgroup$
$begingroup$
Stupid question... but would I plug it in as: (20,000+4n)=17.89648?
$endgroup$
– Gill Dave
Oct 15 '17 at 4:46
$begingroup$
Almost that. Look again.
$endgroup$
– BruceET
Oct 15 '17 at 6:27
1
$begingroup$
Oh my goodness, thank you so much!
$endgroup$
– Gill Dave
Oct 15 '17 at 14:30
add a comment |
$begingroup$
In somewhat improved notation, the PDF table for the random variable $X$ is
k: 0 1 2 3 4
P(X=k): 0.078 0.242 0.337 0.160 0.183
First, notice that $sum_{k=0}^4 P(X=k) = 1,$ as required for a PDF. Then $$E(X) = sum_{k=0}^4 kP(X = k) = 2.128.$$
The profit per order is $29(.29) = $8.41.$ So the profit on the expected $2.128$ orders per customer
is $$17.89648.$
The profit for $n$ customers is $$17.89648n.$ From what you say, I suppose the cost of a campaign reaching $n$ customers
to be $$(20,000 + 4n).$ I will leave it to you to find the number $n$ of
customers to break even, as required.
$endgroup$
In somewhat improved notation, the PDF table for the random variable $X$ is
k: 0 1 2 3 4
P(X=k): 0.078 0.242 0.337 0.160 0.183
First, notice that $sum_{k=0}^4 P(X=k) = 1,$ as required for a PDF. Then $$E(X) = sum_{k=0}^4 kP(X = k) = 2.128.$$
The profit per order is $29(.29) = $8.41.$ So the profit on the expected $2.128$ orders per customer
is $$17.89648.$
The profit for $n$ customers is $$17.89648n.$ From what you say, I suppose the cost of a campaign reaching $n$ customers
to be $$(20,000 + 4n).$ I will leave it to you to find the number $n$ of
customers to break even, as required.
answered Oct 15 '17 at 4:38
BruceETBruceET
35.9k71440
35.9k71440
$begingroup$
Stupid question... but would I plug it in as: (20,000+4n)=17.89648?
$endgroup$
– Gill Dave
Oct 15 '17 at 4:46
$begingroup$
Almost that. Look again.
$endgroup$
– BruceET
Oct 15 '17 at 6:27
1
$begingroup$
Oh my goodness, thank you so much!
$endgroup$
– Gill Dave
Oct 15 '17 at 14:30
add a comment |
$begingroup$
Stupid question... but would I plug it in as: (20,000+4n)=17.89648?
$endgroup$
– Gill Dave
Oct 15 '17 at 4:46
$begingroup$
Almost that. Look again.
$endgroup$
– BruceET
Oct 15 '17 at 6:27
1
$begingroup$
Oh my goodness, thank you so much!
$endgroup$
– Gill Dave
Oct 15 '17 at 14:30
$begingroup$
Stupid question... but would I plug it in as: (20,000+4n)=17.89648?
$endgroup$
– Gill Dave
Oct 15 '17 at 4:46
$begingroup$
Stupid question... but would I plug it in as: (20,000+4n)=17.89648?
$endgroup$
– Gill Dave
Oct 15 '17 at 4:46
$begingroup$
Almost that. Look again.
$endgroup$
– BruceET
Oct 15 '17 at 6:27
$begingroup$
Almost that. Look again.
$endgroup$
– BruceET
Oct 15 '17 at 6:27
1
1
$begingroup$
Oh my goodness, thank you so much!
$endgroup$
– Gill Dave
Oct 15 '17 at 14:30
$begingroup$
Oh my goodness, thank you so much!
$endgroup$
– Gill Dave
Oct 15 '17 at 14:30
add a comment |
Thanks for contributing an answer to Mathematics Stack Exchange!
- Please be sure to answer the question. Provide details and share your research!
But avoid …
- Asking for help, clarification, or responding to other answers.
- Making statements based on opinion; back them up with references or personal experience.
Use MathJax to format equations. MathJax reference.
To learn more, see our tips on writing great answers.
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f2472654%2fbreakeven-point%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown