A manual assembly line is to be designed to make a small consumer product. The work elements, their times, and

precedence constraints are given in the table below. The workers will operate the line for $420$ min per day and must

produce $300$ products per day. A mechanized belt, moving at a speed of $1\mathrm{.}25$ m$/$min$,$ will transport the products between

stations. Previous experience suggests$$that the up time efficiency for the line will be $95\%,$ and repositioning time lost

per cycle will be $0\mathrm{.}03$ min.

a$)$ Detennine the theoretical minimum number of workers on the line. $[2]$

b$)$ Balance the line using the rank positional weight method and calculate its efficiency. $[12)$

Element Time$($Min$.)$ Preceded by Element Time Preceded by

$0\mathrm{.}460\mathrm{.}23$

$20\mathrm{.}770\mathrm{.}34$

$30\mathrm{.}580\mathrm{.}94,9$

$40\mathrm{.}8290\mathrm{.}35,6$

$51\mathrm{.}02,3100\mathrm{.}57,8$