Consider the three station process shown below. The probability of a part being defective at station $1$ is P $1$ and at station $2$ is P $2$ and at station $3$ is P $3.$ All defects from stations $1$ and $2$ are scrapped. Defects from station $3$ are scrapped with probability Q$3,$ reworked at station $1$ with probability Q$1,$ and reworked at station $2$ with probability Q$2.$ Let I denote the input into station $1($also labeled as "Raw Materials" in the figure$)$ and let $O$ denote the total output of good parts from station $3.$

Ra$\text{'}$

Ma

Represent the total steady state output $(O)$ of the process as a function of I,$P1,P2,P3,Q1,Q2,$ and Q$3.$ Show this expression on your work paper that you submit.

Assume the following values for the parameters. $P1=0\mathrm{.}10,P2=0\mathrm{.}20,P3=0\mathrm{.}30,Q1=0\mathrm{.}5,Q2=0\mathrm{.}25,$ and $Q3=0\mathrm{.}25$

For these parameter values what value of I is needed to get an output value of $100?$ Submit that value as your final answer, submit a decimal value with one digit after the decimal point.