Q3) (25 points) A firm has established a distribution network for the supply of a raw material critical to its manufacturing. Currently there are three origins for this raw material, which must be shipped to three manufacturing plants. The current network has the following characteristics:

(a) Calculate a solution using the northwest-corner rule. Calculate the cost of this solution. (b) Calculate the solution using intuitive lowest cost method. Calculate the cost of this solution. (10 points) (c) Using the solution in (c), calculate improvement indices, iterate once. Can you achieve a better solution? If yes, what is the cost of this solution? (10 points)

PLEASE answer as soon as possible.

\begin{tabular}{|l|c|c|c|c|} \hline & Plant 1 & Plant 2 & Plant 3 & SUPPLY \\ \hline Origin I & $7 & $5 & $2 & 30 \\ \hline Origin 2 & $10 & $7 & $3 & 40 \\ \hline Origin 3 & $3 & $8 & $9 & 50 \\ \hline DEMAND & 35 & 45 & 40 & 120/120 \\ \hline \end{tabular} \begin{tabular}{|l|c|c|c|c|} \hline & Plant 1 & Plant 2 & Plant 3 & SUPPLY \\ \hline Origin I & $7 & $5 & $2 & 30 \\ \hline Origin 2 & $10 & $7 & $3 & 40 \\ \hline Origin 3 & $3 & $8 & $9 & 50 \\ \hline DEMAND & 35 & 45 & 40 & 120/120 \\ \hline \end{tabular}