PROBLEM I: In an assembly line, there are $7$ workstations, as shown below. In row $1,$ you are given the processing times in minutes. Row $2$ gives the workstation number. Assume an $8-$hour $(480-$minute$)$ work day.

$\backslash$table$[[5\mathrm{.}6,4\mathrm{.}7,6\mathrm{.}4,6\mathrm{.}8,10\mathrm{.}0,7\mathrm{.}3,2\mathrm{.}9],[1,2,3,4,5,6,7]]$

$(1)$ The output capacity of the assembly line is:

$($a$)32$

$($b$)40$

$($c$)36$

$($d$)48$

$($e$)$ none of the above

$(2)$ The percent of idle time $($rounded to $2$ decimal places$)$ is:

$($a$)27\mathrm{.}84$

$($b$)32\mathrm{.}39$

$($c$)49\mathrm{.}29$

$($d$)37\mathrm{.}57$

$($e$)$ None of the above

$(3)$ If the desired output rate is $32$ units per day, the minimum number of workstations needed is:

$($a$)2($b$)3$

$($c$)4($d$)5$

$($e$)6$

$($b$)$ None of the above

Re$-$organize the workstations so that you can produce at least $32$ units, while minimizing the idle time.

$(4)$ After the re$-$organization, the output capacity of the assembly line is:

$($a$)30$

$($b$)32$

$($c$)24$

$($d$)36$

$($e$)$ None of the above

$(5)$ After, the re$-$organization, the percent of idle time $($rounded to $2$ decimal places$)$ is:

$($a$)13\mathrm{.}84$

$($b$)24\mathrm{.}39$

$($c$)17\mathrm{.}23$

$($d$)8\mathrm{.}56$

$($e$)$ none of the above

PROBLEM II: In an assembly line, there are $7$ workstations, as shown below. In row $1,$ you are given the processing times in minutes. Row $2$ gives the workstation number. Assume an $8-$hour $(480-$minute$)$ work day.

$\backslash$table$[[6\mathrm{.}1,3\mathrm{.}2,8\mathrm{.}4,2\mathrm{.}5,20\mathrm{.}0,1\mathrm{.}4,1\mathrm{.}7],[1,2,3,4,5,6,7]]$

$(6)$ The output capacity of the assembly line is:

$($a$)40$

$($b$)24$

$($c$)16$

$($d$)20$

$($e$)$ none of the above

$(7)$ The percent of idle time $($rounded to $2$ decimal places$)$ is:

$($a$)69\mathrm{.}07($b$)32\mathrm{.}39($c$)34\mathrm{.}25($d$)36\mathrm{.}40($e$)$ none of the above

$(8)$ If the desired output rate is $20$ units per day, the minimum number of workstations needed is:

$(a)3(b)2(c)5(d)4(e)6(b)$ None $of$ the above

$(9)$ If the desired output rate is $20$ units per day, the target cycle time is:

$($a$)32$ minutes $($b$)24$ minutes

$($c$)30$ minutes

$($d$)48$ minutes

$($e$)$ none of the above