Consider the transportation problem in Table 1. Table 1: Data for the transportation problem Demand D1 D2 D3 Supply $5 $1 $7 10 $6 80 $6 $4 $3 $2 $5 75 20 50 55 Supplier S1 S2 S3 Demand (a) Use the least-cost method to find the starting solution (20 marks). (b) Develop the iterations that lead to the optimum solution. (40 marks). (c) Assuming the supplier S3 encounters a technical problem which leads to a shortage of supply, and the original supply of 55 units is reduced to 15 units. Suppose that the penalty costs per unit of unsatisfied demand are $5, $3, and $2 for destinations D1, D2, and D3, respectively. Using the least-cost starting solution, determine all iterations leading to optimum solution. (40 marks).