Question

Find the minimum of f(x,y,z) = x2 + y2 + z2 subject to the two constraints...

Find the minimum of f(x,y,z) = x2 + y2 + z2 subject to the two constraints x + 2y + z = 3 and x - y = 4 by answering following questions

a) write out the lagrange equation involving lagrange multipliers λ(lamba) and μ(mu)

b) solve for lamba in terms of x and y

c) solve for x,y,z using the constraints

d) determine the minimum value

Homework Answers

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Use the method of Lagrange multipliers to find the minimum value of the function f(x,y,z)=x2+y2+z2 subject...
Use the method of Lagrange multipliers to find the minimum value of the function f(x,y,z)=x2+y2+z2 subject to the constraints x+y=10 and 2y−z=3.
Find the minimum of f(x, y, z) = x2 + y2 + z2 subject to the...
Find the minimum of f(x, y, z) = x2 + y2 + z2 subject to the two constraints x + y + z = 1 and 4x + 5y + 6z = 10
Use Lagrange multipliers to find the extremal values of f(x,y,z)=2x+2y+z subject to the constraint x2+y2+z2=9.
Use Lagrange multipliers to find the extremal values of f(x,y,z)=2x+2y+z subject to the constraint x2+y2+z2=9.
Use Lagrange Multipliers to find the extreme values of f(x,y,z) = x2 + 3y subject to...
Use Lagrange Multipliers to find the extreme values of f(x,y,z) = x2 + 3y subject to the constraints x2 + z2 = 9 and 3y2 + 4z2 = 48.
Use the method of Lagrange Multipliers to find the maximum value: f(x,y,z) = x2y2z2 subject to...
Use the method of Lagrange Multipliers to find the maximum value: f(x,y,z) = x2y2z2 subject to the constraint x2+y2+z2=1 no decimals permitted
Using Lagrange multipliers, find the coordinates of the minimum point on the graph of z=x2+y2 subject...
Using Lagrange multipliers, find the coordinates of the minimum point on the graph of z=x2+y2 subject to the constraint 2x+y=20. Lagrange function (use k for lambda) L(x,y,k)= Lx(x,y,k)= Ly(x,y,k)= Lk(x,y,k)= Minimum Point (format (x,y,z)):
Use Lagrange multipliers to find the maximum and minimum values of f(x,y)=x2+5y subject to the constraint...
Use Lagrange multipliers to find the maximum and minimum values of f(x,y)=x2+5y subject to the constraint x2-y2=3 , if such values exist. Maximum = Minimum
Use the method of Lagrange multipliers to find the maximum and minimum values of F(x,y,z) =...
Use the method of Lagrange multipliers to find the maximum and minimum values of F(x,y,z) = 5x+3y+4z, subject to the constraint G(x,y,z) = x2+y2+z2 = 25. Note the constraint is a sphere of radius 5, while the level surfaces for F are planes. Sketch a graph showing the solution to this problem occurs where two of these planes are tangent to the sphere.
Use the Lagrange Multipliers method to find the maximum and minimum values of f(x,y) = xy...
Use the Lagrange Multipliers method to find the maximum and minimum values of f(x,y) = xy + xz subject to the constraint x2 +y2 + z2 = 4.
Calculate ∫ ∫S f(x,y,z)dS for the given surface and function. x2+y2+z2=144, 6≤z≤12; f(x,y,z)=z2(x2+y2+z2)−1.
Calculate ∫ ∫S f(x,y,z)dS for the given surface and function. x2+y2+z2=144, 6≤z≤12; f(x,y,z)=z2(x2+y2+z2)−1.