$2\mathrm{.}9.$ The total processing cost for producing the X $-$Pacer running shoe

in Problem $2\mathrm{.}5$ is $$18.$ The Omega Shoe Company starts production

of $650$ pairs of the shoes weekly, and the average weekly yield is $90\%,$

with $10\%$ defective shoes. One quarter of the defective shoes can be

reworked at a cost of $$3\mathrm{.}75.$

a$.$ Compute the quality$-$productivity ratio $($QPR$).$

b$.$ Compute the QPR if the production rate is increased to $800$

pairs of shoes per week.

c$.$ Compute the QPR if the processing cost in part a$.$ is reduced to

$$16\mathrm{.}50$ and the rework cost to $$3\mathrm{.}20.$

d$.$ Compute the QPR if the product yield in part a$.$ is increased

to $93\%$ good quality.