$2\mathrm{.}2.$ The Backwoods American company in Problem $2\mathrm{.}1$ produces approximately $20,000$ parkas annually. The quality management program the company implemented was able to improve the average percentage of gdod parkas produced by $2\%$ each year, beginning with $83\%$ good$-$quality parkas in Year $1.$ Only about $20\%$ of poor$-$quality parkas can be reworked.

a$.$ Compute the product yield for each of the five years.

b$.$ Using a rework cost of $$12$ per parka, determine the manufacturing cost per good parka for each of the five years. What do these results imply about the company's quality management program?