Question $1(50\%)$ :

You are required to solve the line balancing problem below. Suppose a production line is designed to operate $7\mathrm{.}5$ hours per day and supply a steady demand of $450$ units per day. The line efficiency is assumed to be $100\%.$ The production line performs $14$ tasks. The task operation times $($in minutes$)$ and their precedence relationships are given in Table $1.$ You are required to determine the number of workstations and the assignment of the tasks to the workstations to balance the production line, and meet customer demands by applying the longest$-$task$-$time $($LTT$),$ and the Ranked Positional Weights $($RPW$)$ methods, respectively. You need to present and explain the solution procedures and discuss the results appropriately. Moreover, you are required to discuss line balancing and production levelling methods in broad context to demonstrate the breadth of your knowledge with supporting references.

Table $1.$ Description of the tasks, time and precedence relationships

$\backslash$table$[[$Task Number,Task time $($minutes$),$Preceding tasks$],[$Task $1,0\mathrm{.}32,-],[$Task $2,0\mathrm{.}85,-],[$Task $3,0\mathrm{.}72,-],[$Task $4,0\mathrm{.}41,-],[$Task $5,0\mathrm{.}82,-],[$Task $6,0\mathrm{.}55,-],[$Task $7,0\mathrm{.}44,-],[$Task $8,0\mathrm{.}39,3,2,1$