The data for the second and third questions are given below.

$\backslash$table$[[$Work Element $($k$),$Tek ${?}_{(min)},$Preceded By$],[$A$,2,-],[$B$,1,-],[$C$,3,-],[$D$,4,$A$,$B$],[$E$,2,$B$,$C$],[$F$,1,-],[$G$,2,$E$],[$H$,4,$D$,$G$],[$I$,2,$H$],[$J$,2,$H and J$],[$K$,1,$K$],[$L$,25,],[$T ${?}_{wc},,]]$

$(28$ points$)$ Consider an assembly line in a company which operates $6$ days in a week, one shift a day and the duration of a shift is $8$ hours. $45$min lunch$-$break and $15$min tea$-$break is available for the workers in a shift. The line stops during these breaks. $450$ products are required to be produced on the assembly line in a week. Each station must have a worker and there is $12sec.$ re$-$positioning time. From the historical data of the line, the line efficiency is estimated to be $96\%.$ The following table provides details of the product produced in this assembly line.

a$)$ What is the hourly Production Rate $($Rp$)?(3$ points$)$

b$)$ What is the Cycle Time $($Tc$)?(3$ points$)$

c$)$ What is the Service Time $($Ts$)?(3$ points$)$

d$)$ What is the theoretical minimum number of workers $(w^{**})$ required for the line? $(3$ points$)$

e$)$ Draw the precedence diagram. $(3$ points$)$

f$)$ Balance the line by Ranked Positional Weight $($RPW$)$ Rule, if there is a tie between the work elements, break the ties according to maximum Tek values. $(10$ points$)$

g$)$ Calculate the balance efficiency. $(3$ points$)$