# Math Help - Optimization problems

1. ## Optimization problems

Take an equilateral triangular prism.

if the volume of it is 400 cm^3, what dimensions of the package will use the minimum amount of materials?

I really cant get how to find out the initial equaltion for this, help would be greatly appreciated.

2. Originally Posted by Sky12
Take an equilateral triangular prism.

if the volume of it is 400 cm^3, what dimensions of the package will use the minimum amount of materials?

I really cant get how to find out the initial equaltion for this, help would be greatly appreciated.
(All lengths in cm)

Let the side of the equilateral triangular base be s, and the length of the
prism be l. Then the volume of the prism is sqrt(3)s.l = 400.

The material used for the package is the surface area of the prism, which is:

A(s,l) = 3.s.l+2.sqrt(3)s,

(3 sides s by l, 2 ends in the form of equilateral triangles of side s)

which is to be minimised.

RonL