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a marble company has hired you as their new production manager. your job is to choose the form of packaging for a new product from the five choices below. the package must hold at least 400 cubic inches. the cost of the cardboard for the packaging is $0.02 per square inch.

Solid 1: Volume = 11 * 5 * 7 = 385  cubic inches.  This is less than 400 cubic inches so can't be used.

Solid 2: Volume = 10*10*14 /3 = 466.67

Surface area = 397.32 sq. in.

Cost: 397.32 sq. in. x 0.02 = $7.95

Solid 3: Volume = Pi x 5^2 x 7 = 549.78 cubic inches.

Surface area = 376.99 sq. inches.

Cost = 376.99 x 0.02 = $7.54

Solid 4: Volume = Pi x 5^2 x 15/3 = 392.7 cubic inches. This is less than 400 so can't be used.

Solid 5: Volume = 4/3  Pi x 5^3 = 523.6 cubic inches.

Surface area: 314.16 cubic inches.

Cost: 314.16 x 0.02 = $6.28

unit cost:

Solid 2: 7.95 / 466.67 = $0.017 per cubic inch.

Solid 3: 7.54 / 549.78 = $0.014 per cubic inch.

Solid 5: 6.28 / 523.6 = $0.012 per cubic inch.

Solid 5 is the best option.