Inconsistent lagrange multiplier
$begingroup$
so I have a function $f = 2pi r h$ with $r, h$ as incognites. I want to minimize it.
The restriction
$g = pi r^2 h-0.25$
The problema is that when I do the method I get an inconsistency like:
$$
2 = lambda r
$$
$$
2= lambda pi r
$$
Does someone know why this happen?
derivatives lagrange-multiplier maxima-minima
edited Dec 6 '18 at 5:20
Luca Carai
31119
asked Dec 6 '18 at 5:13
Mel JMel J
65
$endgroup$
add a comment |
$begingroup$
so I have a function $f = 2pi r h$ with $r, h$ as incognites. I want to minimize it.
The restriction
$g = pi r^2 h-0.25$
The problema is that when I do the method I get an inconsistency like:
$$
2 = lambda r
$$
$$
2= lambda pi r
$$
Does someone know why this happen?
derivatives lagrange-multiplier maxima-minima
edited Dec 6 '18 at 5:20
Luca Carai
31119
asked Dec 6 '18 at 5:13
Mel JMel J
65
$endgroup$
add a comment |
$begingroup$
so I have a function $f = 2pi r h$ with $r, h$ as incognites. I want to minimize it.
The restriction
$g = pi r^2 h-0.25$
The problema is that when I do the method I get an inconsistency like:
$$
2 = lambda r
$$
$$
2= lambda pi r
$$
Does someone know why this happen?
derivatives lagrange-multiplier maxima-minima
edited Dec 6 '18 at 5:20
Luca Carai
31119
asked Dec 6 '18 at 5:13
Mel JMel J
65
$endgroup$
so I have a function $f = 2pi r h$ with $r, h$ as incognites. I want to minimize it.
The restriction
$g = pi r^2 h-0.25$
The problema is that when I do the method I get an inconsistency like:
$$
2 = lambda r
$$
$$
2= lambda pi r
$$
Does someone know why this happen?
derivatives lagrange-multiplier maxima-minima
derivatives lagrange-multiplier maxima-minima
edited Dec 6 '18 at 5:20
Luca Carai
31119
asked Dec 6 '18 at 5:13
Mel JMel J
65
edited Dec 6 '18 at 5:20
Luca Carai
31119
asked Dec 6 '18 at 5:13
Mel JMel J
65
edited Dec 6 '18 at 5:20
Luca Carai
31119
edited Dec 6 '18 at 5:20
Luca Carai
31119
edited Dec 6 '18 at 5:20
Luca Carai
31119
31119
asked Dec 6 '18 at 5:13
Mel JMel J
65
asked Dec 6 '18 at 5:13
Mel JMel J
65
asked Dec 6 '18 at 5:13
Mel JMel J
65
65
add a comment |
add a comment |
1 Answer
1
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$begingroup$
HINT: Use $$begin{cases} f_r =2pi h= lambda g_r=lambda 2pi rh\ f_h =2pi r= lambda g_h=pi r^2 \ pi r^2 h=0.25end{cases}$$
answered Dec 6 '18 at 5:44
Thomas ShelbyThomas Shelby
2,525421
$endgroup$
add a comment |
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1 Answer
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1 Answer
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active
oldest
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active
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active
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$begingroup$
HINT: Use $$begin{cases} f_r =2pi h= lambda g_r=lambda 2pi rh\ f_h =2pi r= lambda g_h=pi r^2 \ pi r^2 h=0.25end{cases}$$
answered Dec 6 '18 at 5:44
Thomas ShelbyThomas Shelby
2,525421
$endgroup$
add a comment |
$begingroup$
HINT: Use $$begin{cases} f_r =2pi h= lambda g_r=lambda 2pi rh\ f_h =2pi r= lambda g_h=pi r^2 \ pi r^2 h=0.25end{cases}$$
answered Dec 6 '18 at 5:44
Thomas ShelbyThomas Shelby
2,525421
$endgroup$
add a comment |
$begingroup$
HINT: Use $$begin{cases} f_r =2pi h= lambda g_r=lambda 2pi rh\ f_h =2pi r= lambda g_h=pi r^2 \ pi r^2 h=0.25end{cases}$$
answered Dec 6 '18 at 5:44
Thomas ShelbyThomas Shelby
2,525421
$endgroup$
HINT: Use $$begin{cases} f_r =2pi h= lambda g_r=lambda 2pi rh\ f_h =2pi r= lambda g_h=pi r^2 \ pi r^2 h=0.25end{cases}$$
answered Dec 6 '18 at 5:44
Thomas ShelbyThomas Shelby
2,525421
answered Dec 6 '18 at 5:44
Thomas ShelbyThomas Shelby
2,525421
answered Dec 6 '18 at 5:44
Thomas ShelbyThomas Shelby
2,525421
answered Dec 6 '18 at 5:44
Thomas ShelbyThomas Shelby
2,525421
2,525421
add a comment |
add a comment |
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