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 errors can be detected and eliminated. However, the inspector is paid $$8$ per hour and can inspect units in the process at the rate of $30$ per hour. If no inspector is used and defects are allowed to pass this point, there is a cost of $$10$ per unit to correct the defect later on$.$ Should an inspector be hired?

Design specifications require that a key dimension on a product measure $100+-10$ units. A process being considered for producing this