@17:41 "We're gonna be off by a negative here." The minus sign is superfluous. The constraint, g(x,y), is a homogeneous equation [it's equal to zero]. As such it literally does not matter whether you add or subtract it from the objective function when forming the Lagrangian function, F(x,y,λ). Most mathematicians would write F(x,y,λ) = f(x,y) - λ·g(x,y), where g(x,y) = 100x + 200y - 30000 = 0. Economists have a weird obsession with non-standard notation. They think it enhances job security or something. To an economist the Lagrangian is typically written as F(x,y,λ) = f(x,y) + λ·g(x,y), where g(x,y) = 30000 - 100x - 200y = 0. In this case the minus sign that would typically be in front of λ is distributed across the terms of g(x,y). But even this doesn't make any difference in the solution to the problem because g(x,y) = 0 and because nobody cares about the sign of λ; it's only a parameter guaranteeing that grad f is parallel to grad g. You didn't make a mistake in setting the problem up the way you did in the first place. 😎
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such a good and funny professor..Thanks a lot
Thank you very much, your work is appreciated :)
@17:41 "We're gonna be off by a negative here."
The minus sign is superfluous. The constraint, g(x,y), is a homogeneous equation [it's equal to zero]. As such it literally does not matter whether you add or subtract it from the objective function when forming the Lagrangian function, F(x,y,λ).
Most mathematicians would write F(x,y,λ) = f(x,y) - λ·g(x,y), where g(x,y) = 100x + 200y - 30000 = 0. Economists have a weird obsession with non-standard notation. They think it enhances job security or something. To an economist the Lagrangian is typically written as F(x,y,λ) = f(x,y) + λ·g(x,y), where g(x,y) = 30000 - 100x - 200y = 0. In this case the minus sign that would typically be in front of λ is distributed across the terms of g(x,y). But even this doesn't make any difference in the solution to the problem because g(x,y) = 0 and because nobody cares about the sign of λ; it's only a parameter guaranteeing that grad f is parallel to grad g. You didn't make a mistake in setting the problem up the way you did in the first place. 😎
Explained quite well. Where can one get the book?
A very Great piece.
Absolutely loved the video
don't we need to do the second derivative test with the bordered hessian matrix at the end of each exercise ?
what is is the maximum value of the second problem?
Tysm....this video proves to b very useful for me...😊
Dont you have to take the negative of the objective function since this is a maximization problem?
Please do a video on second order condition?
What textbook are you using to get this theorem?
😄😄😄😄😄thank you ma'am, yo explain in so well!!
Very well explained
Thank you very much
Thanks! But you only solved for critical values, and not optimal quantity.
Q= ALαKβ
C = wL + rK
F(L,K, λ) = ALαKβ + λ(C-wL-rK)
Where r=5; w=10; α=1/2; β=1/2;
How can I find L,K,Q, and λ?
Thanks a lot.
What software do you use to write?
Did u know it?
Thank you love you hug you and appreciate you
so helpful thank you
thank you
You never explained why (3,3) was a point of maximum and not of minimum. You must explain the sufficient conditions as well.
Tysm❤️
Thank you very much. Not making it formal made it interesting. Imagine! Maths? Interesting?
Are u mad women frist you learn
from scipy.optimize import minimize as mimi
sol=mimi(lambda a:2*a[0]*a[1],x0=[1,1],constraints=[{'type':'eq','fun':lambda a:a[0]+a[1]-6}])
print(sol)
message: Optimization terminated successfully
success: True
status: 0
fun: 18.000000357627883
* x: [ 3.000e+00 3.000e+00]*
nit: 3
jac: [ 6.000e+00 6.000e+00]
nfev: 10
njev: 3