Question

The united parcel service has contracted you to design a closed box with a square base that has a volume of 10,000 cubic inches. if they are concerned with minimizing cost of construction of each box, what dimensions should the box be and why?

Answer 1

height: h=V/w/(9w)= V/(9w^2)
surface area: w*9w+ h*(20w)= 9w^2 + 20wV/(9w^2) = 9w^2 + 20/9 V/w
minimum at:
w = cube root of (10/81 V)
dimensions:
w, 9w, V/(9