Problems $2\mathrm{.}5(15$ points$)$

The ABC Company is planning a new product line and a new plant to produce the parts for the line. The product line will include $8$ different models. Annual production of each model is expected to be $900$ units. Each product will be assembled of $180$ components. All processing of parts will be accomplished in the new plant. On average, $6$ processing operations are required to produce each component, and each operation takes an average of $1\mathrm{.}0$min $($including an allowance for setup time and part handling$).$ All processing operations are performed at workstations, each of which includes a production machine and a human worker. The plant operates one $8$ hour shift. Determine the number of $($a$)$ components, $($b$)$ processing operations, and $($c$)$ workers that will be needed to accomplish the processing operations if each worker works $2000h\frac{r}{y}r.$