$2\mathrm{.}13$ Consider a simple three$-$step manufacturing process as illustrated in the given figure. Assuming that demand is $1,000$ units, what is the required input to meet demand? You'll note that the required input is the same if the scrap rates are reversed for processes $1$ and $3.$ Assume that the scrap cost is $$5$ at process $1,$$$10$ at process $2,$ and $$15$ at process $3.$ The defective rates are $3\%,5\%,$ and $7\%,$ respectively. Compute the to tal scrap cost for the given system and the system where the scrap rates are reversed. Which system would be preferred?