If the cost of replacing a defective DVD disk once it has been shipped is $2.00, while the cost of 100% inspection prior to shipment is $.40 each, at what point is he indifferent between 100% inspection and shipment without inspection?
A)0% defectives
B)2% defectives
C)5% defectives
D)20% defectives
E)30% defectives

Question

Quizplus · Accepted Answer

To find the point at which the cost of 100% inspection is the same as the cost of replacing a defective disk, we need to set up an equation:

.40n = 2(1-n)

where n is the percentage of defectives.

Simplifying this equation, we get:

.40n = 2 - 2n

2.4n = 2

n = 2/2.4 = 0.8333

This means that if the percentage of defectives is greater than 83.33% (assuming continuous values), it is more cost-effective to simply replace defective disks as they are discovered rather than inspecting each disk prior to shipment.

To find the answer choice that is closest to 83.33%, we can look at the options provided. 20% defectives is the closest to 83.33%, so the answer is D) 20% defectives.

If the Cost of Replacing a Defective DVD Disk Once