$2\mathrm{.}24$ Suppose that a final assembly is produced by assembling two components. The first component, component A$,$ is produced in$-$house and proceeds through three process steps, blanking, forging, and machining, with scrap estimates of $10\%,15\%,$ and $25\%,$ re$-$ spectively. For every three units of component A produced, two are used in the final as$-$ sembly, and one is set aside to meet spare parts requirements. The second component, component B$,$ used exclusively in the final assembly, is purchased from an outside ven$-$ dor and is inspected upon arrival; $2\%$ fail inspection. One unit of the purchased compo$-$ nent is required for each final assembly. The final assembly process produces $5\%$ scrap. The demand for the spare parts of component A and the final assembly are $1000$ and $5000$ units, respectively. How many units of input are required to produce component A$,$ and how many units must the company buy of component B$?$