Tagged Questions
1
vote
1answer
29 views
What's wrong with this Kuhn-Tucker optimization?
The function $u(x,y,z) = xyz$ is to be maximized, under constraints: $ 0 \le x \le 1, y \ge 2, z \ge 0 $ and $ 4 - x - y - z \ge 0 $
Now I'm not quite sure how to translate the x-constraint into ...
0
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2answers
44 views
Finding constrained optima of $f(x,y) = x^3 - y^3 -x$
For a function $$f(x,y) = x^3 - y^3 -x$$, the minimum and maximum under the constraint $$x^2 + y^2 =1 $$
is searched.
So as usual, my approach is to set up the Lagrangian and the FOC:
$$ L(x,y, ...
0
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0answers
38 views
Minimize a three variable function using Euler-Lagrange theorem
I have to minimize the function $g(x,y,z)=x^2+y^2+2z^2-x-yz$ in two cases. First, with the restriction $x+y+z=35$, and after with $x+y+z\geq35$
I know how to do this using Lagrange multipliers ...
0
votes
0answers
23 views
Trouble with geometrical application of Lagrange multiplier
Let $A\in\mathbb R^{n\times n}$ be positive-definite and $\langle Ax,x\rangle=1$ be the equation of an ellipsoid $M\subset\mathbb R^n$. Use Lagrange multipliers to prove that the greatest distance of ...
0
votes
0answers
212 views
Deriving demand functions given utility
A consumer purchases food $X$ and clothing $Y$. Her utility function is given by: $U(X,Y) = XY +10Y$, income is $\$100$ the price of food is $\$1$ and the price of clothing is $P_y$.
Derive the ...
1
vote
0answers
106 views
Lagrange multipliers for finding geodesics on a sphere
The problem statement, all variables and given/known data
Find the geodesics on a sphere $g(x,y,z)=x^{2}+y^{2}+z^{2}−1=0$
arc-length element $ds=\sqrt{dx^{2}+dy^{2}+dz^{2}}$
Relevant equations
...
1
vote
4answers
353 views
Find an equation of the plane that passes through the point $(1,2,3)$, and cuts off the smallest volume in the first octant. *help needed please*
Find an equation of the plane that passes through the point $(1,2,3)$, and cuts off the smallest volume in the first octant.
This is what i've done so far....
Let $a,b,c$ be some points that the ...
1
vote
4answers
271 views
Use Lagrange multiplier to find absolute maximum and minimum
Use Lagrange multiplier to find absolute maximum and minimum of $f(x,y) =x^2+xy+y^2, x^2+y^2 =8$.
What i've done so far..
$f_x = \lambda g_x \Rightarrow 2x+y =\lambda2x, \\f_y = \lambda g_y ...
