A quality inspector for Alpha-Beta Co. is concerned about the quality of the batch of several thousand blank DVD disks which his company produced this week and is preparing to ship. If the cost of replacing a defective DVD disk once it has been shipped is $2.50, while the cost for 80% inspection prior to shipment is $0.32 each, while the cost of 100% inspection prior to shipment is $0.40 each, at what point is she indifferent between 100% inspection and shipment without inspection?

a. 12.8% defectives
b. 16% defectives
c. 20% defectives
d. 32% defectives

b. 16% defectives

Explanation:

Let the number of units shipped be N

Let the defect rate be y%

Cost of replacing defectives once shipped = (y/100)×N× 2.5  equation (1)

Cost of 100% inspection = N × 0.4 equation (2)

At the indifference point, both costs, that is the replacement cost and inspection cost are equal. Therefore, we make both equations (1) and (2) equal.

N × 0.4 = (y/100)×N× 2.5

100 × 0.4 = y ×2.5

y = 40/2.5 = 16

She is indifferent at 16% defectives

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