This is an extension of the transportation model. . There are now intermediate transshipment points added between the sources (plants) and destinations (retailers). Items being shipped from a Plant (pi) must be shipped to a Warehouse (wj) before being shipped to the Retailer (rk). Each Plant will have an associated supply (si) and each Retailer will have a demand (dk). The number of plants is n, number of warehouses is q and the number of retailers is m. The edges (i,j) from plant (pi)to warehouse (wj) have costs associated denoted cp(i,j). The edges (j,k) from a warehouse (wj)to a retailer (rk) have costs associated denoted cw(j,k). The graph below shows the transshipment map for a manufacturer of refrigerators. Refrigerators are produced at four plants and then shipped to a warehouse (weekly) before going to the retailer.

Part C) warehouse 2 will be open but limit shipments to 100 refrigerators per week. is this feasible? if so what is optimal solution? Using Linear Programming what are the new contraints? Would the W2

Here is my original code. If you could help with Lindo that would be great. thanks!

Lindo Code: Min 10P1W1 +15P1W2 + 11P2W1 + 8P2W2 + 13P3W1 + 8P3W2 + 9P3W3 +14P4W2 + 8P4W3 + 5W1R1 + 6W1R2 + 7W1R3 + 10W1R4 + 12W2R3 + 8W2R4 + 10W2R5 + 14W2R6 + 14W3R4 + 12W3R5 + 12W3R6 + 6W3R7 S.T. P1W1 + P1W2 =100 W1R2 >=150 W1R3 + W2R3 >= 100 W1R4 + W2R4 + W3R4 >= 200 W2R5 +W3R5 >= 200 W2R6 + W3R6 >= 150 W3R7 >= 100 P1W1 + P2W1 + P3W1 - W1R1 - W1R2 - W1R3 - W1R4 >=0 P1W2 + P2W2 + P3W2 + P4W2 - W2R3 - W2R4 - W2R5 - W2R6 >= 0 P3W3 + P4W3 - W3R4 - W3R5 - W3R6 - W3R7 >= 0

Below are the costs of shipping from a plant to a warehouse and then a warehouse to a retailer. Ifit is impossible to ship between the two locations an X is placed in the table cost P1 P2 P3 P4 W1 $10 $11 $13 W2 $15 $8 $8 $14 W3 $8 cost W1 W2 $5 $7 $12 $6 $10 $8 $14 $14 $12 $6 tables below give the capacity of each plant (supply) and the demand for each retailer (per week). P1 150 P2 450 P3 250 P4 Supply 150 Demand 100 150 100 200 200 150 100