**Problem 1: Shortest Path in a Network**The diagram presented is a network graph consisting of seven nodes interconnected by directed edges, each labeled with a numerical value representing the "cost" or "weight" of traversing that edge. Your objective is to find the shortest (minimum cost) path from Node 1 to Node 7.### Node Connections and Costs:- **Node 1**: - Connects to Node 2 with a cost of 5. - Connects to Node 3 with a cost of 6. - Connects to Node 4 with a cost of 6.- **Node 2**: - Connects to Node 3 with a cost of 2.5. - Connects to Node 5 with a cost of 4.- **Node 3**: - Connects to Node 4 with a cost of 3. - Connects to Node 6 with a cost of 2.- **Node 4**: - Connects to Node 6 with a cost of 3.- **Node 5**: - Connects to Node 6 with a cost of 2. - Connects to Node 7 with a cost of 8.- **Node 6**: - Connects to Node 7 with a cost of 7.### Task:Your task is to calculate the shortest path from Node 1 to Node 7. The previously suggested possible answer is a total minimum cost of 16. Use a problem-solving approach similar to the one applied in earlier problems.**Hint**: You may find graph algorithms like Dijkstra’s algorithm useful for solving this problem efficiently. Analyze the given paths and compute the total costs to determine the optimal one.

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Practical Management Science

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ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

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Problem 20P: Julie James is opening a lemonade stand. She believes the fixed cost per week of running the stand...

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Maximal flow problem. Determin the Maximal flow from node 1 to 7

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1 2.5 2 3 2.5 2 3 6 5 2 8 7 7 Find the shortest(min cost) path From Node 1 to Node 7. Possible answer is 16. Try to solve it the same way we did problem 1 and 2.