ers to problems labeled $(A)$ are listed in the appendix.

$($A$)$ A manufacturing plant produces three product lines in one of its plants: A$,$ B$,$ and C Each product line has multiple models: $3$ models within product line A$.5$ models within B$,$ and $7$ within C$.$ Average annual production quantities of model A is $400$ units, $800$ units for model B$,$ and $500$ units for model C$.$ Determine the number of $($a$)$ different product models and $($b$)$ total quantity of products produced annually in this ptant.

Consider product line A in Problem $2\mathrm{.}1.$ Its three models have an average of $46$ components each, and the average number of operations needed to produce each component is $3\mathrm{.}5.$All components are made in the same plant. Determine the total number of $($a$)$ components produced and $($b$)$ operations performed in the plant annually.