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? Youll 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 $$15$ at process $3.$ The defective rates are $3\%,5\%,$ and $7\%,$ respectively. Compute the total scrap cost for the given system and the system where the scrap rates are reversed. Which system would be preferred? $1$ d$13\%23$ d$25\%$ d$37\%2\mathrm{.}14$ Consider Problem $2\mathrm{.}13$ where, in this case, each process is capable of rework. Given the information in the following table, what is the input required to satisfy a demand of $1,000$ units? Process $123$ Defect Rate $3\%5\%7\%$ Rework Rate $60\%75\%80\%$ Suppose that scrap costs are negligible, and rework costs are $$2,$ $$3,$ and $$4,$ respectively. Calculate the rework cost for producing the $1,000$ units. What happens to the rework cost if the scrap rates on processes $1$ and $3$ are reversed? Does this result agree with that of Problem $2\mathrm{.}13?$