id: 06670831
dt: j
an:
au: Premadasa, Kirthi; Martin, Paul; Sprecher, Bryce; Yang, Lai; Dodge,
Noah-Helen
ti: The soda can optimization problem: getting close to the real thing.
so: PRIMUS, Probl. Resour. Issues Math. Undergrad. Stud. 26, No. 7, 694-704
(2016).
py: 2016
pu: Taylor \& Francis, Philadelphia, PA
la: EN
cc: I45 N65 M15
ut: optimization; calculus; modeling
ci:
li: doi:10.1080/10511970.2016.1154631
ab: Summary: Optimizing the dimensions of a soda can is a classic problem that
is frequently posed to freshman calculus students. However, if we only
minimize the surface area subject to a fixed volume, the result is a
can with a square edge-on profile, and this differs significantly from
actual cans. By considering a more realistic model for the can that
consists of six components, including varying wall thickness, and
minimizing the total metal volume, we arrive at an optimal can that has
dimensions more in-line with actual manufactured cans. This model
indicates an optimal radius of 2.83 cm and an overall height of 15.2
cm, which is closer to the dimensions of real cans today than what is
obtained from assuming the can is a right circular cylinder. The
calculations involved would serve as a useful undergraduate modelling
project.
rv: