A beer distributor needs to plan how to make deliveries from its warehouse (node 1) to a supermarket (node 7), as shown in the network below. A graph with 7 nodes and 9 arcs is shown. Node 1 is connected to node 2 by arc of value 3, to node 5 by arc of value 3, and to node 6 by arc of value 11. Node 2 is connected to node 3 by arc of value 4. Node 3 is connected to node 2 by arc of value 4 and to node 4 by arc of value 7. Node 4 is connected to node 3 by arc of value 7, to node 6 by arc of value 5, and to node 7 by arc of value 6. Node 5 is connected to node 6 by arc of value 7. Node 6 is connected to node 4 by arc of value 5, to node 5 by arc of value 7, and to node 7 by arc of value 3. Develop the LP formulation for finding the shortest route from the warehouse to the supermarket. (Let xij represent the flow from node i to node j.) Min        s.t.Node 1 Flows       Node 2 Flows       Node 3 Flows       Node 4 Flows       Node 5 Flows       Node 6 Flows       Node 7 Flows     xij > 0 for all i and j

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Optimization Models

Optimization models are mathematical models that help organizations determine the best way to allocate scarce resources to achieve specific objectives. These models can be used to solve a wide variety of problems, from finding the most efficient route for a delivery truck to determining the optimal mix of products to stock in a store.