A new production process at Firstenlast, Inc. has two in-line stages. The probability of defects occurring in stage 1 is 20%. If there is a defect at stage 1, there is a 30% chance of a defect at stage 2. If there is no defect at stage 1, the probability of a defect at stage 2 is only 10%.
Finished units that only have a stage 1 defect can be repaired at a cost of $7. A stage 2 only defect costs $10 to repair. Items with a stage 1 and a stage 2 defect must be scrapped at a cost of $1 each.
It costs $28 to manufacture and test each unit. The shipping cost is $2 per unit. They sell for $45 each.
a) What percentage of finished units will have the following attributes?
(i) no defects,
(ii) a stage 1 defect only,
(iii) a stage 2 defect only, and
(iv) a stage 1 and a stage 2 defect.
b) What is the expected profit per unit?