Question

There is a 2 percent 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 $10 per hour and could inspect units in the process at the current production rate of 48 per hour.
If no inspector is hired and defects are allowed to pass this point, there is a cost of $11 per defective unit to correct the defects later on.
Assume that the line will operate at the same rate (i.e., the current production rate) regardless of whether the inspector is hired or not.
a. If an inspector is hired, what will be the inspection cost per unit? (Round your answer to 3 decimal places.)
Inspection cost per unit _____________$
b. If an inspector is not hired, what will be the defective cost per unit? (Round your answer to 3 decimal places.)
Defective cost per unit _____________$
c. Should an inspector be hired based on costs alone?

Answer 1

Answer:

A)  $0.208 per unit

B) $0.220 per unit

C) An inspector should be hired

Explanation:

percentage of defect rate = 2% = 0.02

cost of inspector = $10 per hour

production rate = 48 per hour

cost of not hiring an inspector = $11

A) Determine the inspection cost per unit if an inspector is hired

= cost of inspector / production rate

= 10 / 48 = $0.208 per unit

B) Determine the defective cost per unit if an Inspector is not hired

= cost of not hiring an inspector * percentage of defect rate

= 11 * 0.02

= $0.220 per unit

C)   Inspection cost < defective cost   i.e. $0.208 < $0.220  hence an inspector should be hired