There is a $3$ percent error 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 $$11$ per hour and could inspect units in the process at the current production rate of $52$ per hour.

If no inspector is hired and defects are allowed to pass this point, there is a cost of $$12$ 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.$)$

b$.$ If an inspector is not hired, what will be the defective cost per unit? $($Round your answer to $3$ decimal places.$)$

c$.$ Should an inspector be hired based on costs alone?

multiple choice

Yes

No