A company will make a cereal box with whole number dimensions and a volume of 100 cubic centimeters. If cardboard cost $0.05 per 100 square centimeters, what is the least cost to make 100 boxes?

Question

I cannot figure this out

Answer 1

assuming yu plan tu make a rektangular  solid box, best shape=kube

if hav loest area/volume.

for 100 cc, eech side=10 cm.

area=6*100=600

5 sents*600=3000 sents=30$

Answer 2

Volume=l*w*t where l=length, w=width, t=depth or thickness. Factors of 100 are (1,1,100), (1,2,50), (1,4,25), (1,5,20), (1,10,10), (2,2,25), (2,5,10), (4,5,5) representing (t,w,l). Cost c of the box is the surface area=2*0.05(lw+wt+lt)/100. The values of c associated with the factored dimensions are: $0.201, $0.152, $0.129, ..., $0.065. This box has almost cube dimensions, which provides the maximum volume. 5^3=125 which is closest to 100cc. The least cost is 6.5 cents per box and the dimensions are 5cm by 5cm by 4cm. (Surface area 2(25+20+20)=130 sq cm.) 100 boxes cost $6.50.