A workstation has a production rate of $100$ parts$/$hour and runs for $7$ hours. The direct manufacturing cost is $$40/$part$.$ Only $85\%$ of the parts conform to specifications $($first$-$pass yield$).$ From the non$-$conforming parts, $80\%$ can be reworked into an acceptable product, and the rest is scrapped; the cost of this additional processing is $$10/$part$.$

a$.$ How many good parts are produced during the shift?

b$.$ What is the manufacturing cost per shift and per good part produced?

An improvement project reduced variability and the first$-$pass yield increased to $90\%.$ The percent on defective parts that can be reworked remains at $80\%.$ After this improvement:

c$.$ How many good parts are produced per shift?

d$.$ What is the manufacturing cost per good part produced, in total per good part produced?

e$.$ What is the reduction in manufacturing cost per part $($in US$ and in percent$)?$

f$.$ What is the increase in production per shift $($in units and in percent$)?$