Question

Apply Lagrange multipliers to solve the problem. Find the
dimensions of the box with a volume of 8 ?3 that has minimal
surface area.

Answer #1

Using Lagrange multipliers, find the dimensions and volume of
the largest rectangular box in the first octant with 3 faces in the
coordinate planes, one vertex at the origin and an opposite vertex
on the paraboloid z = 1 - x2 - y2.

Use Lagrange multipliers to find the dimensions of the
rectangular box of maximum volume,
with faces parallel on the coordinate planes, that can be
inscribed in the first octant of the
ellipsoid 4x^2 + y^2 +4z^2=192

Use
Lagrange multipliers to find the dimensions of a right circular
cylinder with volume Vo cubic units and minimum surface area.
r(Vo)=
h(Vo)=
Thank you!

Determine the dimensions of a rectangular box without lid, of
maximum volume if the total surface is fixed at 64 cm2 . Solve
without using Lagrange multipliers.

Use Lagrange multipliers to find the volume of the largest
rectangular box with edges parallel to the axes that can be
inscribed in the ellipsoid. 9x^2 + 9y^2 + 4z^2 = 324

Use Lagrange multipliers to find the volume of the largest
rectangular box in the first octant with three faces in the
coordinate planes and one vertex in the given plane.
x + 3y + 4z = 9

Use Lagrange multipliers to find the volume of the largest
rectangular box in the first octant with three faces in the
coordinate planes and one vertex in the given plane.
x + 4y + 3z = 12

Find the dimensions of a box with a top that has a volume of
1000 cubic centimeters that minimizes the possible surface area

Use Lagrange multipliers to solve the given optimization
problem. HINT [See Example 2.]
Find the maximum value of f(x, y) = xy subject to y = 12 −
x2.
fmax =
Also find the corresponding point (x, y). (x, y) =

Find the dimnesions of the box with the volume 5832cm^3 that has
minimal surface area

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