Plainwell Polymers is going to producing the main dashboard structure for a new car

design. The dashboard will be produced in three colors with expected daily demand

as follows:

Black: $370$ units$/$day

Grey: $165$ units$/$day

Tan: $185$ units$/$day

The injection$-$molding machine can produce a total of $975$ parts per day running $24$

hours per day.

It costs Plainwell $$1,050$ to set up each color for producition and the daily holding

cost for each part is $$0\mathrm{.}18.$ What is the length of the lowest cost cyclic schedule

$($ignoring setup time constraints$)$ in days?