John Deere$’$s remanufacturing division collects old John Deere equipment returned to dealers $($for a credit$),$ which is then inspected, cleaned, and rehabilitated by replacing failed components with new ones. The remanufacturing facility receives shipments from dealerships around the country,

which immediately transfer returned equipment to the remanufacturing facility.

On average, there are $336$ pieces of used equipment transferred to the remanufacturing facility each week. Since dealerships do not coordinate their shipments, the remanufacturing facility receives many shipments in a day. The

standard deviation of the time between shipment arrivals is $1$ hour. The remanufacturing facility is open $24$ hours per day, $7$ days per week.

Repairs are completed by a technician, and it takes a technician on average $4$ 

hours to completely repair a returned piece of equipment. However, the remanufacturing process is fraught with uncertainty. Some returned equipment

is in good shape and requires minimal repair while others require repairs that are

much more involved. The standard deviation of the time to complete a repair is

$4$ hours. Currently, the remanufacturing facility staffs $15$ technicians during each

shift.

A$.$ On average, how many returned pieces of equipment are at the

remanufacturing facility to be repaired $($including pieces that are waiting

and are being repaired$)?$

B$.$ How long $($in hours$)$ on average does a piece of returned equipment spend

at the remanufacturing facility $($assume that repaired equipment is

immediately shipped to a dealer$)?$

C$.$ On average, how many facility staffs are idle?

D$.$ John Deere pays each technician $$40/$hour$.$ John Deere also incurs a

holding cost of $$5$ for each hour each piece of equipment is held in storage,

including pieces being repaired. What is the total hourly cost $($combining

labor and holding costs$)?$