a$.$ The initial transport cost after allocation using northwest corner method

The cost of transferring one unit from factory W to outlets at $($A$,$ B$,$ and C$)$ are $4,3,$ and $3$ rupees respectively.

The cost of transferring one unit from factory Y to outlets at $($A$,$ B$,$ and C$)$ are $6,7,$ and $6$ rupees respectively.

The cost of transferring one unit from factory Z to outlets at $($A$,$ B$,$ and C$)$ are $8,2,$ and $5$ rupees respectively.

The total cost of transport using the northwest corner method is $4+3+6+7+8+2+5=35$ rupees.

b$.$ The initial transport cost after allocation using intuitive lowest cost method

The cost of transferring one unit from factory W to outlets at $($A$,$ B$,$ and C$)$ are $4,3,$ and $3$ rupees respectively.

The cost of transferring one unit from factory Y to outlets at $($A$,$ B$,$ and C$)$ are $6,7,$ and $6$ rupees respectively.

The cost of transferring one unit from factory Z to outlets at $($A$,$ B$,$ and C$)$ are $8,2,$ and $5$ rupees respectively.

The total cost of transport using the intuitive lowest cost method is $3+4+6+2+7+5+8=35$ rupees.

c$.$ The low cost option between those and apply steppingstone method to compute the optimum cost of transport.

The steppingstone method is a heuristic method that is used to find an approximate solution to a problem. In this method, we first select a set of feasible solutions, then we select the best solution from this set, and finally we improve this solution until we find the optimal solution.