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The Holix Corporation has two separate processing centers for credit applications. Each

credit application passes through three steps: step $1-$background credit check, step $2-$

credit risk profile analysis, and step $3-$credit level approval and communication to client.

The processing time for each of the stages is $20$ minutes for credit check, $50$ minutes for

credit risk profile analysis, and $14$ minutes for credit approval and communication. The

set$-$up time between successive applications for each step is $10$ minutes. While both

processing center take similar steps, they each deal with different types of applications:

processing center $1$ evaluates residential customers and processing center $2$ evaluates com$-$

mercial customers.

$5$a$.$ Each of the two processing centers is organized in exactly the same manner

and receives the same average number of applications per day. For example,

processing center $1$ gets about $30$ applications per $8-$hour day. The first step in

center $1$ has $2$ employees working in parallel. The second step has $4$ employees

working in parallel, and the third step has $2$ employees working in parallel. What

is the average lead time to process an application through all three steps in each

processing center?