Q$7\mathrm{.}6($Static$)$ Quality Check $[7\mathrm{.}6]$

Once the raw materials are collected, a single flow unit manufacturing process comprises three sequential steps:

$-$ Step $1$ consumes large amounts of an expensive paint

$-$ Step $2$ is the bottleneck

$-$ Step $3$ has a large amount of idle time

There exists a $20$ percent chance at each step to produce a defect, and raw materials have a $20$ percent chance to have a defect. However, defects are not immediately observable. A defect reduces the value of the final product to zero; that is$,$ a product with just one defect has no value and must be discarded. Consider the following statements.

The process presently is capacity constrained. Which of the following statements best captures good advice on where to locate a single inspection point?

The only inspection point should be before step $1.$

If the focus is on cost savings of the expensive paint, the inspection should occur before step $1.$ If the focus is on flow rate, the inspection point should be before step $2.$ If the focus is on cost savings of the expensive paint, the inspection should occur before step $2.$ If the focus is on flow rate, the inspection point should be before step $3.$

The only inspection point should be before step $3.$