Question

Postal regulations specify that a parcel sent by parcel post may have a combined length and girth of no more than 130 in. Find the dimensions of a cylindrical package of greatest volume that may be sent through the mail, using the method of Lagrange multipliers

Answer 1

Answer :-

Consider the method of Lagrange multipliers can be extended to solve problems with multiple constraints using a similar argument. Consider a paraboloid subject to two line constraints that intersect at a single point. As the only feasible solution, this point is obviously a constrained extremum. However, the level set of is clearly not parallel to either constraint at the intersection point instead, it is a linear combination of the two constraints' gradients.