A product is manufactured in a two-stage process, the stages being designated $\mathrm{A}$ and $\mathrm{B}$.

Each process has two machines, named $A 1$ and $A 2$ for process $A$, and B1 and B2 for process B.

Each unit of finished product must pass through either one of the two machines in process $A$, and then through either one of the two machines in process B. ($50 \%$ go through A1 and $50 \%$ through A2. Similarly for B1 and B2.)

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How many different ways may a product be manufactured? The probabilities of a defective product from each machine are as follows: 2% for A1, 6% for A2, 4% for B 1, 2% for B2. The defectives are thrown out as they occur. What is the probability of a perfect item being produced? The total production is 10,000 items started every year. The loss on each defective item is $10, and the profit on each item is $80. The expected net profit is 69 $