A company will make a cereal box with whole number dimensions and a volume of 100 cubic centimeters. if carboard cost $0.05 per 100 square cm, what is he least cost to make 100 boxes

Possible dimension of a box with a volume of 100 cubic cm

10 x 10 x 1 = 100

10 x 5 x 2 = 100

5 x 5 x 4 = 100

Surface area:

10 x 10 x 1 dimensions:

10 x 10 = 100 x 2 = 200 sq. cm

10 x 1 = 10 x 4 = 40 sq. cm

240 sq. cm * $0.05 / 100 sq. cm = $0.12 per box

0.12 per box * 100 boxes = $12

10 x 5 x 2 dimension

10 x 5 = 50 x 2 = 100 sq. cm

10 x 2 = 20 x 2 = 40 sq. cm

5 x 2 = 10 x 2 = 20 sq. cm

160 sq. cm * $0.05/100 sq. cm = $0. 08 per box

0.08 per box * 100 boxes = $8

5 x 5 x 4 dimension

5 x 5 = 25 x 2 = 50 sq. cm

5 x 4 = 20 x 4 = 80 sq. cm

130 sq. cm * $0.05/100 sq. cm = $0.065 per box

0.065 per box * 100 boxes = $6.50

The best dimension to use to have the least cost to make 100 boxes is 5 x 5 x 4. It only costs $6.50 to make 100 boxes.