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5 September, 08:44

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

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  1. 5 September, 10:55
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    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.
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