There is a 3% defect rate at a specific point in a production process. If an inspector is placed at this point, all the defects can be detected and eliminated. The inspector would cost $8 per hour and could inspect units in the process at the current production rate of 30 per hour. If no inspector is hired and defects are allowed to pass this point, there is a cost of $10 per defective unit to correct the defects later on. Assume that the line will operate at the same rate (i. e., the current production rate) regardless of whether the inspector is hired or not.
A. If an inspector is hired, what will be the inspection cost per unit?
B. If an inspector is not hired, what will be the defective cost per unit?
C. Should an inspector be hired based on costs alone?

A. $2.67 per unit

B. $0.3 per unit

C. Yes

Explanation:

A. Calculation for what will be the inspection cost per unit If an inspector is hired,

Using this formula inspection cost

Inspection cost=Cost of inspector/inspection rate per hour

Inspection cost = 8/30

Inspection cost = $2.67 per unit

Therefore what will be the inspection cost per unit If an inspector is hired is $2.67 per unit

B. Calculation for what will be the defective cost per unit If an inspector is not hired,

Using this formula formula

No inspection =(Defective average *Inspection rate * Correction cost) /Inspection rate

Let plug in the formula

No inspection=0.03*30 per hour *$10 each/30 per hour

No inspection =9/30

No inspection = $0.3 per unit

Therefore what will be the defective cost per unit If an inspector is not hired is $0.3 per unit

C. Yes the inspector should be hired based on the costs alone.

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