$2\mathrm{.}1.($A$)$ A manufacturing plant produces three product lines in one of its plants: A$,$ B$,$ and C$.$ Each product line has multiple models: $5$ models within product line $A,3$ models within $B,$ and $4$ within $C.$ Total annual production quantity of all models of product $A$ is $2,000$ units, $1,500$ units for product $B,$ and $800$ units for product $C.$ Determine the number of $(a)$ different product models and $($b$)$ total quantity of products made annually in this plant.

Consider product line A in Problem $2\mathrm{.}1.$ Its $5$ models have an average of $27$ components each, and the average number of operations needed to produce each component is $4\mathrm{.}5.$ All components are made in the same plant.

Determine the total number of $($a$)$ components produced and $($b$)$ operations performed in the plant annually for product line $A.$