Poehling Medical Center has a single operating room that is used by local physicians to perform surgical procedures. The cost of using the operating room is accumulated by each patient procedure and includes the direct materials costs $($drugs and medical devices$),$ physician surgical time, and operating room overhead. On January $1$ of the current year, the annual operating room overhead is estimated to be:

The overhead costs will be assigned to procedures, based on the number of surgical room hours. Poehling Medical Center expects to use the operating room an average of eight hours per day, seven days per week. In addition, the operating room will be shut down two weeks per year for general repairs.

a$.$ Determine the predetermined operating room overhead rate for the year. Round your answer to the nearest dollar.

b$.$ Bill Harris had a six$-$hour procedure on January $22.$ How much operating room overhead would be charged to his procedure, using the rate determined in part $($a$)?$ Round your answer to the nearest dollar.

c$.$During January, the operating room was used $230$ hours. The actual overhead costs incurred for January were $$68,900.$ Determine the overapplied operating overhead or underapplied operating overhead for the period. Enter your answer as a positive number. Round your answer to the nearest dollar.