a$)(8$ pts$.)$ Running this line as a push system, and with a single machine in

each stage, what is the maximum number of units the line can produce in

an $18-$hour $($yes$,$ they work from $6$AM to $12$AM$)$ day? $($Hint: maximize the

throughput while assuring the CT is $3-$hours or shorter.$)$

b$)(16$ pts$.)$ Mr$.$ Aramazo has been approached by John O$$Cush$,$ an

entrepreneur and a long$-$time customer. Mr$.$ O$$Cush believes he can

increase the sales to $300$ units per day easily. The first thought that crosses

Mr$.$ Aramazo$$s mind is that he needs to set up a number of parallel lines,

consisting of a single machine per stage but he quickly figures that$$s not

practical for many reasons. Instead, he decides to add parallel machines in

each stage but preserve the structure of a single line. Under the same $3-$

hour cycle$-$time constraint, what are the minimum number of machines at

each stage to produce the desired $300$ units in $18$ hours? $($Hint: If there are

multiple solutions with the same minimum total number of machines,

choose the one that also minimizes the cycle$-$time.$)$

c$)(8$ pts$.)$ What$$s the cycle time of the line with multiple machines per stage

designed in part b$?$

d$)(8$ pts$.)$ Interpret the results obtained in parts b and c$,$ in comparison to

running multiple independent lines $($with a single machine in each stage$)$ in

parallel. What factors contribute to the efficiencies you observe?