Mixing
Minimise $C(x,y)=11x+3y$ subject to the constraints.
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 '18 at 19:42
Ernie060
2,555319
asked Nov 15 '18 at 19:14
John Lee
11
add a comment |
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 '18 at 19:42
Ernie060
2,555319
asked Nov 15 '18 at 19:14
John Lee
11
add a comment |
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 '18 at 19:42
Ernie060
2,555319
asked Nov 15 '18 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 '18 at 19:42
Ernie060
2,555319
asked Nov 15 '18 at 19:14
John Lee
11
edited Nov 15 '18 at 19:42
Ernie060
2,555319
asked Nov 15 '18 at 19:14
John Lee
11
edited Nov 15 '18 at 19:42
Ernie060
2,555319
edited Nov 15 '18 at 19:42
Ernie060
2,555319
edited Nov 15 '18 at 19:42
Ernie060
2,555319
2,555319
asked Nov 15 '18 at 19:14
John Lee
11
asked Nov 15 '18 at 19:14
John Lee
11
asked Nov 15 '18 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 '18 at 11:27
Farid Hasanov
13
add a comment |
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1 Answer
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1 Answer
1
active
oldest
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active
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active
oldest
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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 '18 at 11:27
Farid Hasanov
13
add a comment |
What is your constraint on g(x,y)? There should be some equality or inequality, associated with that equation.
answered Nov 21 '18 at 11:27
Farid Hasanov
13
add a comment |
What is your constraint on g(x,y)? There should be some equality or inequality, associated with that equation.
answered Nov 21 '18 at 11:27
Farid Hasanov
13
What is your constraint on g(x,y)? There should be some equality or inequality, associated with that equation.
answered Nov 21 '18 at 11:27
Farid Hasanov
13
answered Nov 21 '18 at 11:27
Farid Hasanov
13
answered Nov 21 '18 at 11:27
Farid Hasanov
13
answered Nov 21 '18 at 11:27
Farid Hasanov
13
13
add a comment |
add a comment |
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