Solve by hand.

4. Consider the assignment problem formulation of Option 2 for the Better Products Co. problem presented in the following table. Table. Cost table for the assignment problem formulation of Option 2 for the Better Products Co. Problem Assignee 2a (Plant) 2b 3 1 820 820 800 800 740 2 810 810 870 870 900 Task (Product) 3 840 840 M M 810 4 960 960 920 920 840 (a) Reformulate this problem as an equivalent transportation problem with three sources and five destinations by constructing the appropriate parameter table. (b) Convert the optimal solution for this assignment problem into a complete BF solution (including degenerate basic variables) for the transportation problem formulated in part (a). Specifically, apply the "General Procedure for Constructing an Initial BF Solution". For each iteration of the procedure, rather than using any of the three alternative criteria presented for step 1, select the next basic variable to correspond to the next assignment of a plant to a product given in the optimal solution. When only one row or only one column remains under consideration, select the remaining basic variables. (c) Verify that the optimal solution for this assignment problem actually is optimal by applying just the optimality test portion of the transportation simplex method to the complete BF solution obtained in part (b). (d) Now reformulate this assignment problem as an equivalent transportation problem with five sources and five destinations by constructing the appropriate parameter table. Compare this transportation problem with the one formulated in part (a). (e) Repeat part (b) for the problem as formulated in part (d). Compare the BF solution obtained with the one from part (b). 4. Consider the assignment problem formulation of Option 2 for the Better Products Co. problem presented in the following table. Table. Cost table for the assignment problem formulation of Option 2 for the Better Products Co. Problem Assignee 2a (Plant) 2b 3 1 820 820 800 800 740 2 810 810 870 870 900 Task (Product) 3 840 840 M M 810 4 960 960 920 920 840 (a) Reformulate this problem as an equivalent transportation problem with three sources and five destinations by constructing the appropriate parameter table. (b) Convert the optimal solution for this assignment problem into a complete BF solution (including degenerate basic variables) for the transportation problem formulated in part (a). Specifically, apply the "General Procedure for Constructing an Initial BF Solution". For each iteration of the procedure, rather than using any of the three alternative criteria presented for step 1, select the next basic variable to correspond to the next assignment of a plant to a product given in the optimal solution. When only one row or only one column remains under consideration, select the remaining basic variables. (c) Verify that the optimal solution for this assignment problem actually is optimal by applying just the optimality test portion of the transportation simplex method to the complete BF solution obtained in part (b). (d) Now reformulate this assignment problem as an equivalent transportation problem with five sources and five destinations by constructing the appropriate parameter table. Compare this transportation problem with the one formulated in part (a). (e) Repeat part (b) for the problem as formulated in part (d). Compare the BF solution obtained with the one from part (b).