SOLVE YOUR HANDWR$$TTEN $.$Consider a workstation with $11$ machines $($in parallel$),$ each requiring one hour of process

time per job 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 two hours. Currently it is just

over three 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 cost $$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?