Transcript Document

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