Three products are produced on the same line. Task times are shown in Table $2.$ One half of demand is for product $A.$ The other one half of demand is evenly split between products $B$ and $C.$

Table $2$: Task times for Problem $5.$

$\backslash$table$[[$Task$,\backslash$table$[[$Immediate$],[$Predecessors$]],\backslash$table$[[$Product$],[$A$]],\backslash$table$[[$Product$],[$B$]],\backslash$table$[[$Product$],[$C$]]],[1,-,30,25,35],[2,1,15,10,10],[3,1,5,7,5],[4,1,40,40,45],[5,4,50,45,45],[6,4,30,40,40],[7,2,3,15,15,20],[8,5,7,65,60,65],[9,8,25,25,0],[10,6,50,50,60],[11,9,10,45,40,40],[12,11,5,5,5],[]]$

a$.$ Find a line balance for which no workstation has an average work requirement in$.$ excess of $100$ units per product produced $(1$ points$)$

b$.$ Identify the bottleneck workstation $(1$ points$)$

c$.$ Find a repeating cycle or product order entry onto the line that smooths the production rate of the bottleneck workstation without building unnecessary inventories or shortages for any product during the cycle $(1$ poins$)$