Problem $2.$Consider the following tasks for an assembly line operation to be used to produce $144000$ units of a product per year.

Task $=12345678910$

Task Time $($min$.)$Immediate $=0\mathrm{.}60\mathrm{.}40\mathrm{.}90\mathrm{.}30\mathrm{.}20\mathrm{.}70\mathrm{.}50\mathrm{.}60\mathrm{.}40\mathrm{.}7$Predecessors $=-112234,53,57,86,9$

a$)$ Draw the precedence diagram

b$)$ Suppose, the assembly line will be operated $8$ hours per day and $300$ days per year $($excluding holidays$).$ Determine the theoretical number of stations to minimize the balance delay with the ideal cycle time that meets the demand.

c$)$ Determine the balance delay for part $($b$)$

d$)$ Balance the line with Largest Candidate Rule.

e$)$ Balance the line with Ranked Positional Weighted Method.

f$)$ Balance the line with Kilbridge and Wester Method

g$)$ Determine the number of stations and the balance delay for each solution above.