Use the method of Lagrange Multipliers to find the dimensions of a right-circular cylinder with volume V0 cubic units and minimize the surface area.

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Example 1

• Use the method of Lagrange Multipliers to find
  the dimensions of a right-circular cylinder with
  volume V0 cubic units and minimize the surface
  area.

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Example 2

• The material for the base of an open box costs
  1.5 times as much as the material for the sides.
  Use Lagrange Multipliers to find the dimensions
  of the box of largest volume that can be made for
  a fixed cost C.

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Example 3

• Use Lagrange Multipliers to prove that the
  product of three positive numbers x, y, and z,
  whose sum has the constant value S, is a maximum
  when the three numbers are equal.

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Your Problem

• Use the method of Lagrange Multipliers to find
  the shortest distance between the origin and the
  plane ax by cz d.