Word Problem- Find the dimensions of a box of maximum values

Question

A package may be sent by mail only if the sum of its height and the perimeter of the base is not more than 64 inches. Find the dimensions of the box of maximum volume that can be sent. The base of the box is a rectangle with a length equal to two times its width. Round to tenths.

Function:

Dimensions:

Domain:

Range:

Answer 1

V=hlw= h2w^2

l=2w

h+2(l+w)=64

h+2(2w+w)=64

h+6w=64

h= 64-6w

V= (64-6w)2w^2= 128w^2-12w^3

V' =256w -36w^2=0

2w(128-18w)=0

w = 128/18= 64/9= 7.1 inches wide

l=2w =14.2 inches long

h=64-6(64/9)=64-128/3=about 64-42.7= 21.3 inches high

7.1 by 14.2 by 21.3 in.

0<w<32/3=10 2/3

0<l<64/3= 21 1/3

0<h<64