$1\mathrm{.}1$ A small electrical appliance is to be produced on a single$-$model assembly line. The work content of assembling the product has been reduced to the work elements listed in Table A$.$ The table also lists the times for each element and the precedence order in which they must be performed. The line is to be balanced for an annual demand of $150000$ units each year. The line will operate $50$ week a year, $5$ straight shifts per week. These shifts take a duration of $8$ hours per day in a shift, however, there is $30$ minutes break in it$.$ There will be one worker per station. Previous experience suggests that the uptime efficiency for the line will be $83\%,$ and repositioning time lost per cycle will be $0\mathrm{.}03$min.

Table A:

$\backslash$table$[[\backslash$table$[[$Symbol: Work$],[$element$]],$Description,Tek $($min$),\backslash$table$[[$Must be$],[$preceded By$.]]],[$A$,$Place frame in work holder and clamp,$0\mathrm{.}3,-],[$B$,\backslash$table$[[$Assemble plug, grommet to power$],[$cord$]],0\mathrm{.}3,-],[$C$,$Assemble brackets to frame,$0\mathrm{.}7,$A$],[$D$,$Wire power cord to motor,$0\mathrm{.}4,$A$,$ B$],[$E$,$Wire power cord to switch,$0\mathrm{.}3,$B$],[$F$,$Assemble mechanism plate to bracket,$0\mathrm{.}11,$C$],[$G$,$Assemble blade to bracket,$0\mathrm{.}32,$C$],[$H$,$Assemble motor to brackets,$0\mathrm{.}7,$C$,$ D$],[$I$,$Align blade and attach to motor,$0\mathrm{.}29,$F$,$ G$,$ H$],[$J$,$Assemble switch to motor bracket,$0\mathrm{.}38,$E$,$ H$],[$K$,$Attach cover, inspect, and test,$0\mathrm{.}5,$I, J$],[$L$,$Place in tote pan for packing,$0\mathrm{.}12,$K$]]$

Requirements:

a$)$ How would you design the Precedence diagram for the above?

$(10)$

b$)$ Determine the cycle time $($Tc$)?$

$(4)$

c$)$ Determine the minimum number of workers required on the line.

$(4)$

d$)$ Determine the service time $($Ts$)$ to which the line must be balanced.

$(2)$

$[20]$