$(5)$ The assembly line process for a manufacturing company requires the completion of eight tasks to assemble one unit of a product. The diagram below shows the tasks, precedent relationships, and task times in seconds. The VP of Operations sets a target throughput of $400$ units per day. The company's assembly line operates $7\mathrm{.}2$ hours a day for five days a week.

$5$a$)$ Ignoring the throughput, what is the minimum cycle time? $5$b$)$ Ignoring the throughput, what is the maximum cycle time?

$5$c$)$ What is the cycle time $($in seconds$/$unit$)$ to achieve the target throughput?

$5$d$)$ What is the cycle time $($in min$/$unit$)$ to achieve the target throughput?

$5$e$)$ What is the minimum number of workstations?

$5$f$)$ What is the total time available during each cycle time? $5g)$ What is the total idle time during each cycle time?

$5$h$)$ What is the assembly line efficiency?

$5$i$)$ What is the balance delay?

$5$j$)$ Use the shortest task time first decision rule to bal$-$

ance the assembly line. $5k)$ Use the longest task time first decision rule to balance the assembly line.

ANSWERS

$5$a$)26$ seconds$/$unit

$5$b$)148$ seconds$/$unit

$5$c$)64\mathrm{.}80$ seconds$/$unit

$5$d$)1\mathrm{.}08mi\frac{n}{u}$nit

$5$e$)3$ workstations

$5$f$)194\mathrm{.}4$ seconds

$5$ g$)46\mathrm{.}4$ seconds

$5$h$)76\mathrm{.}13\%$

$5$i$)23\mathrm{.}87\%$

$5$j$)$ Shortest task time first decision rule

$\backslash$table$[[$Workstation$,$Tasks,Total Time,Idle Time$],[1,$A$,$ D$,$ E$,55,9\mathrm{.}80],[2,$G$,$ F$,$ B$,63,1\mathrm{.}80],[3,$C$,$ H$,30,34\mathrm{.}80],[$Total$,,148,46\mathrm{.}40]]$

$5$k$)$ Longest task time first decision rule. Note that four workstations are needed.

$\backslash$table$[[$Workstation$,$Tasks,Total Time,Idle Time$],[1,$G$,$ A$,39,25\mathrm{.}80],[2,$B$,$ D$,44,20\mathrm{.}80],[3,$E$,$ F$,$ C$,45,19\mathrm{.}80],[4,$H$,20,44\mathrm{.}80],[$Total$,,148,111\mathrm{.}20]]$

Screens $5-6$ of $12$

I need full explanations please