Question: Problem 2 Consider the following transportation problem with the goal of minimizing total cost: Dest. 2 $1 Dest. 1 $5 $8 $4 500 Source 1

Problem 2 Consider the following transportation

Problem 2 Consider the following transportation problem with the goal of minimizing total cost: Dest. 2 $1 Dest. 1 $5 $8 $4 500 Source 1 Source 2 Source 3 Demand $9 Dest. 3 $5 $10 $8 200 Dest. 4 $3 $4 $2 400 Supply 300 800 500 $3 500 The cost ($/ unit) for transporting from source i to destination j is given in the table. The demand for each destination and the supply from each source is also given in the demand row and the supply column, respectively. a) Is this a balanced transportation problem? Why? If it is not balanced, modify the transportation table to make it balanced. b) Use the Least Cost method to find an initial solution to the problem. What is the total cost? c) Use Vogel's Approximation method to find an initial solution to the problem. What is the total cost in this case? d) Check the optimality of the initial solution obtained by Vogel's approximation method (in part c). Is this an optimal solution? Why

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