There are two assembly lines, as shown in the diagram below, each with $6$ stations. The

auto is required to go through from all of these $6$ stations from left to right. Nodes

represent stations. The assembly time at each station is shown at each node. The entering

and exit times for an auto are also given. The transfer time is represented at the edges

when an auto moves to next station on a different line. There is no transfer time if it stays

on the same line. Determine which stations to choose from lines $1$ and $2$ to minimize total

time through the factory. Also compute the optimal value in terms of time. Use Dynamic

Programming Approach. You need to calculate fi$[$j$],$ li$[$j$],$ f$*,$ l$*$ and the

optimal path.