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: Origin 1 Origin 2 Origin 3 DEMAND Plant 1 $7 $10 $3 35 Plant 2 $5 $7 $8 45 Plant 3 $2 $3 $9 40 SUPPLY 30 40 50 120/120 (a) Calculate a solution using the northwest-corner rule. Calculate the cost of this solution. (5 points) (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)