Consider a workstati

time per job ach in parallel$),$ each requiring one hour of $11$ machines per for with $c_e^2=5.$ Each machine costs $$10,000.$ Orders for jobs arrive at a rate of $10$ per hour with $c_a^2=1$ 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 $m_r$ and $m_f$ are reduced, but $\frac{m_r}{m_f}$ remains the same. This costs $$8,000$ and does not improve the average process time but does reduce $c_e^2$ to one.

$($b$)$ Add another machine to the workstation at a cost of $$10,000.$ The new machine is identical to existing machines, so $t_e=1$ and $c_e^2=5.$

$($c$)$ Modify the existing machines to make them faster without changing the SCV$,$ at a cost of $$8,500.$ The modified machines would have $t_e=0\mathrm{.}96$ and $c_e^2=5.$

What is the best option?