Minimise $C(x,y)=11x+3y$ subject to the constraints.
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Minimise $C(x,y)=11x+3y$ subject to the constraints $ g(x,y)=-3x^2-3y^2+10xy $ and $xgeq 0, ygeq 0$.
I started solving using this Lagrange multiplier, but the constraint set is not compact, right? So, how can I argue whether the critical point is a maximum or a minimum or a saddle point?
lagrange-multiplier constraints
edited Nov 15 at 19:42
Ernie060
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asked Nov 15 at 19:14
John Lee
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Minimise $C(x,y)=11x+3y$ subject to the constraints $ g(x,y)=-3x^2-3y^2+10xy $ and $xgeq 0, ygeq 0$.
I started solving using this Lagrange multiplier, but the constraint set is not compact, right? So, how can I argue whether the critical point is a maximum or a minimum or a saddle point?
lagrange-multiplier constraints
edited Nov 15 at 19:42
Ernie060
2,520319
asked Nov 15 at 19:14
John Lee
11
add a comment |
up vote
0
down vote
favorite
up vote
0
down vote
favorite
Minimise $C(x,y)=11x+3y$ subject to the constraints $ g(x,y)=-3x^2-3y^2+10xy $ and $xgeq 0, ygeq 0$.
I started solving using this Lagrange multiplier, but the constraint set is not compact, right? So, how can I argue whether the critical point is a maximum or a minimum or a saddle point?
lagrange-multiplier constraints
edited Nov 15 at 19:42
Ernie060
2,520319
asked Nov 15 at 19:14
John Lee
11
Minimise $C(x,y)=11x+3y$ subject to the constraints $ g(x,y)=-3x^2-3y^2+10xy $ and $xgeq 0, ygeq 0$.
I started solving using this Lagrange multiplier, but the constraint set is not compact, right? So, how can I argue whether the critical point is a maximum or a minimum or a saddle point?
lagrange-multiplier constraints
lagrange-multiplier constraints
edited Nov 15 at 19:42
Ernie060
2,520319
asked Nov 15 at 19:14
John Lee
11
edited Nov 15 at 19:42
Ernie060
2,520319
asked Nov 15 at 19:14
John Lee
11
edited Nov 15 at 19:42
Ernie060
2,520319
edited Nov 15 at 19:42
Ernie060
2,520319
edited Nov 15 at 19:42
Ernie060
2,520319
2,520319
asked Nov 15 at 19:14
John Lee
11
asked Nov 15 at 19:14
John Lee
11
asked Nov 15 at 19:14
John Lee
11
11
add a comment |
add a comment |
1 Answer
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What is your constraint on g(x,y)? There should be some equality or inequality, associated with that equation.
answered Nov 21 at 11:27
Farid Hasanov
13
New contributor
Farid Hasanov is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
add a comment |
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
0
down vote
What is your constraint on g(x,y)? There should be some equality or inequality, associated with that equation.
answered Nov 21 at 11:27
Farid Hasanov
13
New contributor
Farid Hasanov is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
add a comment |
up vote
0
down vote
What is your constraint on g(x,y)? There should be some equality or inequality, associated with that equation.
answered Nov 21 at 11:27
Farid Hasanov
13
New contributor
Farid Hasanov is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
add a comment |
up vote
0
down vote
up vote
0
down vote
What is your constraint on g(x,y)? There should be some equality or inequality, associated with that equation.
answered Nov 21 at 11:27
Farid Hasanov
13
New contributor
Farid Hasanov is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
What is your constraint on g(x,y)? There should be some equality or inequality, associated with that equation.
answered Nov 21 at 11:27
Farid Hasanov
13
New contributor
Farid Hasanov is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
answered Nov 21 at 11:27
Farid Hasanov
13
New contributor
Farid Hasanov is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
answered Nov 21 at 11:27
Farid Hasanov
13
answered Nov 21 at 11:27
Farid Hasanov
13
13
New contributor
Farid Hasanov is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
New contributor
Farid Hasanov is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
Farid Hasanov is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
add a comment |
add a comment |
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