A production process at Firsten Last, Inc. has two in-line stages. The probability of defects occurring in stage 1 is 25%. If there is a defect at stage 1, there is a 60% 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 $19 to manufacture and $3 to test each unit. The shipping cost is $2 per unit. They sell for $48 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?