Fdtxjr

Decoding assembly instructions in a Game Boy disassembler

Is it true that real estate prices mainly go up?

What to do when during a meeting client people start to fight (even physically) with each others?

Unreachable code, but reachable with exception

Why do Australian milk farmers need to protest supermarkets' milk price?

Replacing Windows 7 security updates with anti-virus?

Latest web browser compatible with Windows 98

Is it illegal in Germany to take sick leave if you caused your own illness with food?

What has been your most complicated TikZ drawing?

What is the blue range indicating on this manifold pressure gauge?

Identifying the interval from A♭ to D♯

Want to switch to tankless, but can I use my existing wiring?

Force user to remove USB token

What wound would be of little consequence to a biped but terrible for a quadruped?

Counter-example to the existence of left Bousfield localization of combinatorial model category

Sword in the Stone story where the sword was held in place by electromagnets

US to Europe trip with Montreal layover - is 52 minutes enough?

Humans have energy, but not water. What happens?

Touchscreen-controlled dentist office snowman collector game

Time travel short story where dinosaur doesn't taste like chicken

The three point beverage

Does anyone draw a parallel between Haman selling himself to Mordechai and Esav selling the birthright to Yaakov?

Do f-stop and exposure time perfectly cancel?

How do anti-virus programs start at Windows boot?

How would Jack allocate his time to maximize his pleasure?

How to solve Linear programs of the form Maximize vHow would I answer this question? (Reworded)How to maximize the sum of vectors in target direction.How would you mathematically formulate this as an optimization problem?Is there a vehicle routing problem without time and cost constraints, whose objective is to maximize revenue?How do I maximize the objective $0 x_1 + 0 x_2 + dots + 0 x_n$ in linear programming?How would I determine how large an M/M/c queue grows after a certain amount of time?How to maximize the infinity norm over a convex region?How many boxes of each mixture should the company make to maximize profit? Linear Programming ProblemHow can I maximize the probability?

0

$begingroup$

Jack is an aspiring freshmen at a university. He realizes that “all work and no play make Jack a dull boy.” As a result, Jack wants to apportion his available time of about $10$ hours a day between work and play. He estimates that play is twice as much as fun as work. He also wants to study at least as much as he plays. However, Jack realizes that if he is going to get all his homework assignment done, he cannot play more than $4$ hours a day. How would Jack allocate his time to maximize his pleasure from both work and play?

linear-programming operations-research

share|cite|improve this question

edited Mar 10 at 22:11

Rodrigo de Azevedo

13k41960

asked Mar 10 at 20:53

Shereen AshrafShereen Ashraf

1

New contributor

Shereen Ashraf is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  A few comments: 1. You should probably make some comments about what you know, and what attempts you think might be worthwhile. Otherwise, the question risks being downvoted and/or closevoted. 2. Does study count as work, I presume? 3. One approach that I recommend is to try some different numbers out, and see how they work. Let work be worth $1$ "funit" ("fun unit") per hour, and play be worth 2 funits per hour. What division permits the greatest number of funits?
  $endgroup$
  – Brian Tung
  Mar 10 at 21:02
  

  
  
  
  

add a comment | 

0

$begingroup$

Jack is an aspiring freshmen at a university. He realizes that “all work and no play make Jack a dull boy.” As a result, Jack wants to apportion his available time of about $10$ hours a day between work and play. He estimates that play is twice as much as fun as work. He also wants to study at least as much as he plays. However, Jack realizes that if he is going to get all his homework assignment done, he cannot play more than $4$ hours a day. How would Jack allocate his time to maximize his pleasure from both work and play?

linear-programming operations-research

share|cite|improve this question

edited Mar 10 at 22:11

Rodrigo de Azevedo

13k41960

asked Mar 10 at 20:53

Shereen AshrafShereen Ashraf

1

New contributor

Shereen Ashraf is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  A few comments: 1. You should probably make some comments about what you know, and what attempts you think might be worthwhile. Otherwise, the question risks being downvoted and/or closevoted. 2. Does study count as work, I presume? 3. One approach that I recommend is to try some different numbers out, and see how they work. Let work be worth $1$ "funit" ("fun unit") per hour, and play be worth 2 funits per hour. What division permits the greatest number of funits?
  $endgroup$
  – Brian Tung
  Mar 10 at 21:02
  

  
  
  
  

add a comment | 

$begingroup$

Jack is an aspiring freshmen at a university. He realizes that “all work and no play make Jack a dull boy.” As a result, Jack wants to apportion his available time of about $10$ hours a day between work and play. He estimates that play is twice as much as fun as work. He also wants to study at least as much as he plays. However, Jack realizes that if he is going to get all his homework assignment done, he cannot play more than $4$ hours a day. How would Jack allocate his time to maximize his pleasure from both work and play?

linear-programming operations-research

share|cite|improve this question

edited Mar 10 at 22:11

Rodrigo de Azevedo

13k41960

asked Mar 10 at 20:53

Shereen AshrafShereen Ashraf

1

New contributor

Shereen Ashraf is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

$endgroup$

share|cite|improve this question

edited Mar 10 at 22:11

Rodrigo de Azevedo

13k41960

asked Mar 10 at 20:53

Shereen AshrafShereen Ashraf

1

New contributor

Shereen Ashraf is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

share|cite|improve this question

edited Mar 10 at 22:11

Rodrigo de Azevedo

13k41960

asked Mar 10 at 20:53

Shereen AshrafShereen Ashraf

1

New contributor

Shereen Ashraf is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

edited Mar 10 at 22:11

Rodrigo de Azevedo

13k41960

edited Mar 10 at 22:11

Rodrigo de Azevedo

13k41960

asked Mar 10 at 20:53

Shereen AshrafShereen Ashraf

1

New contributor

Shereen Ashraf is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

asked Mar 10 at 20:53

Shereen AshrafShereen Ashraf

1

1 Answer
1

active

oldest

votes

0

$begingroup$

Let's write $w$ for the number of hours the Jack works each day, $p$ for the number of hours that Jack plays each day, and $e$ for the amount of enjoyment that Jack gets each day.

$(1)$ Jack has $10$ hours in the day, so $$0 leq w leq 10, 0 leq p leq 10, w + p = 10.$$

$(2)$ Jacks says that play is twice as enjoyable as work, so $$e = w + 2p.$$

$(3)$ Jack says that he wants to work for at least as long as he plays, so $$p leq w.$$

$(4)$ Jack says that he needs to work for at least $4$ hours each day, so $$4 leq w leq 10.$$

We can rearrange $(1)$ and substitute it into $(2)$ to get $e = p + 10$, so we'll maximize the amount of enjoyment exactly when we maximize the amount of play.

Rearranging $(3)$ and substituting it into $(1)$ gives $0 leq p leq 5$. Taking $(w,p) = (5,5)$ satisfies all conditions $(1)$ - $(4)$. We cannot take any higher value of $p$, and a lower one would decrease the enjoyment.

Therefore, Jack should work for $5$ hours and play for $5$ hours.

share|cite|improve this answer

answered Mar 10 at 21:42

Joseph MartinJoseph Martin

587217

$endgroup$

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
);



);

Shereen Ashraf is a new contributor. Be nice, and check out our Code of Conduct.

draft saved

draft discarded

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

Name

Email

Required, but never shown

StackExchange.ready(
function ()
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3142886%2fhow-would-jack-allocate-his-time-to-maximize-his-pleasure%23new-answer', 'question_page');

);

Post as a guest

Name

Email

Required, but never shown

0

$begingroup$

Let's write $w$ for the number of hours the Jack works each day, $p$ for the number of hours that Jack plays each day, and $e$ for the amount of enjoyment that Jack gets each day.

$(1)$ Jack has $10$ hours in the day, so $$0 leq w leq 10, 0 leq p leq 10, w + p = 10.$$

$(2)$ Jacks says that play is twice as enjoyable as work, so $$e = w + 2p.$$

$(3)$ Jack says that he wants to work for at least as long as he plays, so $$p leq w.$$

$(4)$ Jack says that he needs to work for at least $4$ hours each day, so $$4 leq w leq 10.$$

We can rearrange $(1)$ and substitute it into $(2)$ to get $e = p + 10$, so we'll maximize the amount of enjoyment exactly when we maximize the amount of play.

Rearranging $(3)$ and substituting it into $(1)$ gives $0 leq p leq 5$. Taking $(w,p) = (5,5)$ satisfies all conditions $(1)$ - $(4)$. We cannot take any higher value of $p$, and a lower one would decrease the enjoyment.

Therefore, Jack should work for $5$ hours and play for $5$ hours.

share|cite|improve this answer

answered Mar 10 at 21:42

Joseph MartinJoseph Martin

587217

$endgroup$

add a comment | 

0

$begingroup$

Let's write $w$ for the number of hours the Jack works each day, $p$ for the number of hours that Jack plays each day, and $e$ for the amount of enjoyment that Jack gets each day.

$(1)$ Jack has $10$ hours in the day, so $$0 leq w leq 10, 0 leq p leq 10, w + p = 10.$$

$(2)$ Jacks says that play is twice as enjoyable as work, so $$e = w + 2p.$$

$(3)$ Jack says that he wants to work for at least as long as he plays, so $$p leq w.$$

$(4)$ Jack says that he needs to work for at least $4$ hours each day, so $$4 leq w leq 10.$$

We can rearrange $(1)$ and substitute it into $(2)$ to get $e = p + 10$, so we'll maximize the amount of enjoyment exactly when we maximize the amount of play.

Rearranging $(3)$ and substituting it into $(1)$ gives $0 leq p leq 5$. Taking $(w,p) = (5,5)$ satisfies all conditions $(1)$ - $(4)$. We cannot take any higher value of $p$, and a lower one would decrease the enjoyment.

Therefore, Jack should work for $5$ hours and play for $5$ hours.

share|cite|improve this answer

answered Mar 10 at 21:42

Joseph MartinJoseph Martin

587217

$endgroup$

add a comment | 

$begingroup$

Let's write $w$ for the number of hours the Jack works each day, $p$ for the number of hours that Jack plays each day, and $e$ for the amount of enjoyment that Jack gets each day.

$(1)$ Jack has $10$ hours in the day, so $$0 leq w leq 10, 0 leq p leq 10, w + p = 10.$$

$(2)$ Jacks says that play is twice as enjoyable as work, so $$e = w + 2p.$$

$(3)$ Jack says that he wants to work for at least as long as he plays, so $$p leq w.$$

$(4)$ Jack says that he needs to work for at least $4$ hours each day, so $$4 leq w leq 10.$$

We can rearrange $(1)$ and substitute it into $(2)$ to get $e = p + 10$, so we'll maximize the amount of enjoyment exactly when we maximize the amount of play.

Rearranging $(3)$ and substituting it into $(1)$ gives $0 leq p leq 5$. Taking $(w,p) = (5,5)$ satisfies all conditions $(1)$ - $(4)$. We cannot take any higher value of $p$, and a lower one would decrease the enjoyment.

Therefore, Jack should work for $5$ hours and play for $5$ hours.

share|cite|improve this answer

answered Mar 10 at 21:42

Joseph MartinJoseph Martin

587217

$endgroup$

share|cite|improve this answer

answered Mar 10 at 21:42

Joseph MartinJoseph Martin

587217

answered Mar 10 at 21:42

Joseph MartinJoseph Martin

587217

answered Mar 10 at 21:42

Joseph MartinJoseph Martin

587217