A community for students.
Here's the question you clicked on:
 0 viewing
anonymous
 one year ago
image attached
anonymous
 one year ago
image attached

This Question is Closed

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.1Never did these before but I think the budget constraint must be \[60G+6M \le 450\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Yeah. Im unsure about the parts B and C though

Astrophysics
 one year ago
Best ResponseYou've already chosen the best response.1\[\nabla f(x,y) = \lambda \nabla g(x,y)~~~~~\text{and}~~~~~g(x,y) = k\] this is the lagrange multiplier, where g(x,y) = k would be the constraint.

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.1We have inequalities as constraints and it must be solved over integers right ?

Astrophysics
 one year ago
Best ResponseYou've already chosen the best response.1Yeah that sounds good I think

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.1The regular lagrange multipliers method wont work here

Astrophysics
 one year ago
Best ResponseYou've already chosen the best response.1What if we just say 60G + 6M = 450 as the budget constraint

Astrophysics
 one year ago
Best ResponseYou've already chosen the best response.1Then we can set up our langranian as \[L(G,M, \lambda) = G^{1/2}+M^{1/2}+\lambda(45060G6M)\]

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.1then we can use the plain old lagrange multipliers but the problem doesn't say he spends full 450, so don't you think we're changing the problem by simplifying it ?

Astrophysics
 one year ago
Best ResponseYou've already chosen the best response.1Well it says endowment of 450 dollars that he spends on buying games and digital music, it's sort of sounds like he is spending all of it...but you could be right to, not sure.

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.1http://mat.gsia.cmu.edu/classes/QUANT/NOTES/chap4/node6.html

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.1your budget for a week is $450 doesn't necessarily mean you will be spending all of it, it just means that you cannot exceed $450. if this problem is from equality constraints then ofcourse equality constraint makes sense. otherwise it doesn't

Astrophysics
 one year ago
Best ResponseYou've already chosen the best response.1You're right I made an assumption haha.

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.1I mean, the optimal utility need not happen on the surface of g(x,y) = k, it "can" happen anywhere inside the solid g(x,y) <= k.

Astrophysics
 one year ago
Best ResponseYou've already chosen the best response.1Yes, that's right. So it seems this requires an extra step then from the link you provided, checking the complementarity conditions

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.1yeah we need to include constraints for nonnegativity too

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.1Maximize \(U(G,M)=G^{1/2}+M^{1/2}\) subject to : \(60G+6M \le 450\) \(G \le 0\) \(M\le 0\)

Astrophysics
 one year ago
Best ResponseYou've already chosen the best response.1So it's kind of like solving for two constraints \[L(G,M, \lambda_1, \lambda_2) = G^{1/2}+M^{1/2}+\lambda_1(G)+\lambda_2(M) \]

Astrophysics
 one year ago
Best ResponseYou've already chosen the best response.1But you still have the optimality conditions

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.1idk, never worked langrange multipliers with inequality constraint

Astrophysics
 one year ago
Best ResponseYou've already chosen the best response.1Yeah I'm just sort of reading the link you sent, never seen this before either

Astrophysics
 one year ago
Best ResponseYou've already chosen the best response.1https://www.youtube.com/watch?v=3VQBVf6Tr3Y https://www.youtube.com/watch?v=uuXSTsrFok
Ask your own question
Sign UpFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.