Part A: Determine the number of refrigerators to be shipped from the plants to the warehouses and then warehouses to retailers to minimize the cost. Formulate the problem as a linear program with an objective function and all constraints. Determine the optimal solution for the linear program using any software you want. What are the optimal shipping routes and minimum cost?

Part B: Due to old infrastructure Warehouse 2 is going to close eliminating all of the associated routes. What is the optimal solution for this modified model? Is it feasible to ship all the refrigerators to either warehouse 1 or 3 and then to the retailers without using warehouse 2? Why or why not?

Part C: Instead of closing Warehouse 2 management has decide to keep a portion of it open but limit shipments to 100 refrigerators per week. Is this feasible? If so what is the optimal solution when warehouse 2 is limited to 100 refrigerators?

. Transshipment Model (10 points) This is an extension of the transportation model. There are now intermediate transshipment points added between the sources (plants) and destinations (retailers). tems being shipped from a Plant (pi) must be shipped to a Warehouse (w) before being shipped to the Retailer (). Each Plant will have an associated supply (s) 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 (ij) from plant (pi)to warehouse (w) 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. R1 R2 P1 W1 R3 P2 W2 R4 P3 R5 W3 P4 R6 R7 Below are the costs of shipping from a plant to a warehouse and then a warehouse to a retailer. If it is impossible to ship between the two locations an X is placed in the table W1 10 $11 $13 W2 $15 $8 $8 $14 W3 cost P1 P2 P3 P4 $9 $8 R1 R2 R3 R4 R5 R6 R7 cost W1 W2 $10 $12 S8 $10 $12 $12 $14 $14 The tables below give the capacity of each plant (supply) and the demand for each retailer (per week) P1 150 P4 150 P2 P3 450 250 R1 R2 150 R3 100 R6 R7 100 R4 R5 200 Demand 100 200 150 Part A: Determine the number of refrigerators to be shipped from the plants to the warehouses and then warehouses to retailers to minimize the cost. Formulate the problem as a linear program with an objective function and all constraints. Determine the optimal solution forthe linear program using any software you want. What are the optimal shipping routes and minimum cost? Part B: Due to old infrastructure Warehouse 2 is going to close eliminating all of the associated routes What is the optimal solution for this modified model? Is it feasible to ship all the refrigerators to either warehouse 1 or 3 and then to the retailers without using warehouse 2? Why or why not? Part C: Instead of closing Warehouse 2 management has decide to keep a portion of it open but limit shipments to 100 refrigerators per week. Is this feasible? If so what is the optimal solution when warehouse 2 is limited to 100 refrigerators? Note: Include a copy of the code for all parts of the