Consider the assembly line balancing problem described in the table below:

$\backslash$table$[[$Task$,\backslash$table$[[$Task Time$],[($min$.)]],\backslash$table$[[$Immediate$],[$Predecessors$]]],[1,10,-],[2,14,1],[3,8,1],[4,5,3],[5,26,2],[6,9,2],[7,11,4,5],[8,13,6,7],[9,22,8],[10,21,4],[11,19,9,10],[12,17,4,11]]$

a$.$ Develop a network for this assembly operation.

b$.$ Using the ranked positional weight technique, determine the resulting balance using a cycle time of $40$ minutes.

c$.$ Determine the number of work stations needed and the total idle times from part $($b$).$