Brief calc- A parcel delivery service will deliver a package only if the length plus the girth (distance aroun

A parcel delivery service will deliver a package only if the length plus the girth (distance around) does not exceed 120 inches. Find the maximum volume of a rectangular box with square ends that satisfies the delivery company's requirements.



Maximum Volume =Brief calc- A parcel delivery service will deliver a package only if the length plus the girth (distance aroun
length = h

base = s



h + 4s = 120



Volume V = hs^2

V(s) = s^2(120 - 4s)

= 120s^2 - 4s^3



V'(s) = 240s - 12s^2 = 0

s = 0 or s = 20

V''(s) = 240 - 24s

V''(20) = -240 ... thus maximum



h = 40

V = 40 * 20 * 20 = 16,000 cu inches





搂Brief calc- A parcel delivery service will deliver a package only if the length plus the girth (distance aroun
lets call the lengt L and the widht W

L%26gt;W

2L+2W+L=120 (at the point of the maximum volume)

3L = 120-2W

L = 40 - 2/3W

the volume of the box (with square ends) is:

Volume = L*W*W becaus (L%26gt;W)

Volume = L*W^2 = 40-2/3W * W^2

Volume is maximum when the derivative is 0

But, i dont feel like deriving that one now, so just plot it on you calculater and look for the maximum :-P