$1.$ Consider a workstation with $11$ machines, each requiring one hour of process time per job with an SCV of $5.$ Each machine costs $$10,000.$ Jobs arrive at a rate of $10$ per hour with SCV equal to $1$ and they must be filled.$$ 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 this$).$ Analyze the following options and determine which is best for reducing average response time.

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a$)$ Perform more preventive maintenance at a cost of $$8000($over lifetime of the machines$).$ The effect of this on tr and tf is that ultimately ce$2$ is reduced to $1.$

b$)$ Add another identical machine to the workstation at a cost of $$10,000.$

c$)$Modify the existing machines to make them faster without changing the SCV$,$ at a cost of $$8500.$ The modified machines would have te $=0\mathrm{.}96$ hours and ce$2=5.$