Company X manufactures memory chips in lots of 10 at stage 1. In stage 2 each lot is further processed. From experience, it is known at stage 1 that...

Company X manufactures memory chips in lots of 10 at stage 1. In stage 2 each lot is further processed. From experience, it is known at stage 1 that 80% of the lots are "good" and 20% are "bad". Good lots have exactly 1 defective chip and bad lots have exactly 5 defective chips. In the standard procedure at stage 2, the good lots require $1000 of processing to yield 10 acceptable chips while bad lots require $4000 to yield 10 acceptable chips.

a) What is the expected value or average cost at stage 2 per lot?

b) Alternatively, the company can rework each batch (both good and bad) at a cost of $1000 that always produces a good batch that makes it ready for the $1000 processing. What is the expected cost at the end of stage 2 for this procedure?

c) Alternatively, for $100 a technician can sample 1 chip from each batch in an attempt to determine if it is good or a bad batch. If the sample chip is bad, the whole lot is reworked at a cost of $1000 (as in b) to guarantee a good lot for stage 2 with the usual $1000 processing. If the sample is good it is put into the standard procedure as in part a). What is the average cost of a lot in this case?