Q$3-$ Consider a workstation with $11$ machines $($in parallel$),$ each requiring one hour of process time per job with $C_q^2=5.$ 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 $($you can check it$).$

Analyze the following options for reduce average response time and select the best option: $(2$ Points$)$

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

b$)$ Modify the existing machines to make them faster without changing the SCV$,$ at a cost of $$8,000.$ The modified machines would have $t_c=0\mathrm{.}96$ and $C_{,}^2=5(10$ Points$)$

c$)$ Perform more preventive maintenance so that the costs $$9,000$ and does not improve the average process time but reduce the $C_6^2$ to one. $(10$ Points$)$