Question

Postal regulations specify that a parcel sent by priority mail may have a combined length and girth of no more than 132 in. Find the dimensions of a rectangular package that has a square cross section and largest volume that may be sent by priority mail. Hint: The length plus the girth is 4x + l.

Answer 1

v = 11264 in^3

Explanation:

4 x + l =132

l=132- 4 x

v= h x^ 2

= x ^ 2 (132 - 4 x )

= 132 x ^ 2 - 4 x^3

= 4 ( 33 x^2 - x ^3)

d v/d x = 4 (66 x - 3 x^2)

= 12 x ( 22 - x)

d v/d x = 0

when x = 0 or 22

So

h = 132 - 4 *22 = 44

So if the package is 44*16*16

v = 11264 in^3

So 4 x+l >= 132 But it should be minimum if 4 x+l contain smaller value