Consider a workstation with $11$ machines $($in parallel$),$ each requiring one hour of process

time per job with $2=5.$ Each machine costs $$10,000.$ Orders for jobs arrive at a rate of $10$

per hour with $2=1$ and must be filled. Management has specified a maximum allowable

average response time $($i$.$e$.,$ time a job spends at the station$)$ of $2$ hours. Currently it is just over

$3$ hours $($check it$).$

Analyze the following options for reducing average response time.

$($a$)$ Perform more preventive maintenance so that $$ and $$ are reduced, but $$

$$

remains

the same. This costs $$8,000$ and does not improve the average process time but does reduce $2$

to one.

$($b$)$ Add another machine to workstation at a cost of $$10,000.$ The new machine is identical to

existing machines, so $=1$ and $2=5.$

What is the best option?