Test: Math Modeling

1.

A beauty supply company manufactures a variety of brushes. Quality control engineers work to ensure that the defected brushes in the factory will be detected prior to shipping them. It is estimated that approximately 0.2% of the brushes made will be defected. Tests can be done individually on the brushes or on batches of the brushes. If the test on a batch of brushes fails, it means that one or more of the brushes in that particular batch are defected. The estimated cost is 4 cents for a single brush, and  cents for a group of  brushes. If a batch fails then all brushes in that batch must be tested individually. Find the most cost-effected quality control procedure for detecting defected brushes.

By testing brush batches in groups of 9 will reduce testing costs without sacrificing the quality. 

By testing brush batches in groups of 10 will reduce testing costs without sacrificing the quality. 

By testing brush batches in groups of 12 will reduce testing costs without sacrificing the quality. 

By testing brush batches in groups of 15 will reduce testing costs without sacrificing the quality. 

By testing brush batches in groups of 20 will reduce testing costs without sacrificing the quality. 

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