IE $4339$ Fall $2024$ Homework #$2$ Due on Thursday, Oct. $10($submit to Canvas by midnight$)$ Problem $1(20$ points$)$ Consider a line of three identical single$-$machine stations in series. Assume the same parameters for each workstation, i$.$e$.,,,.$ The rate of arrival to the first workstation is $$ with a CV of $.$ Find the total cycle time. $$ Problem $2(30$ points$)$ Consider a single$-$machine workstation. Parts arrival at a rate of $15$ parts$/$hr$.$ Arrival CV is $0\mathrm{.}5.$ The station has a mean effective process time $3$ mins and the standard deviation is also $3$ mins. Assume an M$/$M$/1$ queue, compute $,$ CT and WIP. How would these numbers change if we added an identical machine into the workstation. $$ Problem $3(20$ points$)$ Consider a line with two single$-$machine workstations. Arrival rate to the line is $1\mathrm{.}5$ jobs$/$hr and $=1\mathrm{.}6.$ The first machine has $0=35$ mins, $0=0\mathrm{.}8,$ MTTF $=70$ hrs$,$ MTTR $=3\mathrm{.}5$ hrs$.=1.$ The second machine has $0=30$ mins, $0=1\mathrm{.}2,$ MTTF $=5$ hrs$,$ MTTR $=20$ mins hrs$.=1.$ Find $$ and $$ for both machines. If we need to reduce the $$ for the second machine to be $2,$ how does it impact the throughput?