Consider the assignment problem formulation of Option 2 for the Better Products Co. problem presented in Table 8.29.

(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 given in Sec. 8.3 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” given in Sec. 8.2. 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, use step 4 to select the remaining basic variables.

(c) Verify that the optimal solution given in Sec. 8.3 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).

D,I