1,2,3 are supply; 4,5,6,7 are demand nodes. Costs of each arc are given. Solve the minimum cost flow problem and find the optimal solution by using network simplex algorithm. Show each step clearly.
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1,2,3 are supply; 4,5,6,7 are demand nodes. Costs of
each arc are given. Solve the minimum...
Question 4 (20 marks) Let N be the network below, where ax and y are the...
Question 4 (20 marks) Let N be the network below, where ax and y are the source and sink respectively, and the arc S capacities are shown next to each arc. An initial flow of this network is given in parentheses 3(0) 6(0) 5(0) 4(0) 3(1) 2(0) X 2(1) 2(0) 3(1), 5(1) 4(0) 2(2) 2.5(1) V Starting from the given flow, use the labelling algorithm to find a maximum flow in N. Show every stage of the algorithm. State the...
4. Given a network of 8 nodes and the distance between each node as shown in Figure 1: 4 1 7 0 4 4 6 6 Figure 1: Network graph of 8 nodes a) Find the shortest path tree of node 1 to all the other nod...
4. Given a network of 8 nodes and the distance between each node as shown in Figure 1: 4 1 7 0 4 4 6 6 Figure 1: Network graph of 8 nodes a) Find the shortest path tree of node 1 to all the other nodes (node 0, 2, 3, 4, 5, 6 and 7) using Dijkstra's algorithm. b) Design the Matlab code to implement Dijkstra's algorithm
4. Given a network of 8 nodes and the distance between each...
Trees and Heaps 1. Show that the maximum number of nodes in a binary tree of...
Trees and Heaps 1. Show that the maximum number of nodes in a binary tree of height h is 2h+1 − 1. 2. A full node is a node with two children. Prove that the number of full nodes plus one is equal to the number of leaves in a nonempty binary tree. 3. What is the minimum number of nodes in an AVL tree of height 15? 4. Show the result of inserting 14, 12, 18, 20, 27, 16,...
A network map is given in the Excel file. a) Use the table in the Excel...
A network map is given in the Excel file. a) Use the table in
the Excel file to find the fastest route from point A to point H.
For full credit, you must include the completed table in your
answer and show all possible solved and unsolved nodes in each step
until you solve for point H. b) What nodes do you pass through
along the fastest route from A to point H?
1 Problem 2 Network Map (all node...
In-Class Assignment - Transportation Algorithm The table below provides information (names, supply, demand, and cost/unit) for...
In-Class Assignment - Transportation Algorithm The table below provides information (names, supply, demand, and cost/unit) for a transportation problem involving three warehouses and three customers. Using the information, set up and show an initial solution using the North West Corner (NWC) method and using a dummy row or column if needed. After that, answer the questions that follow the table. Customer 1 Customer 2 Customer 3 Supply Warehouse 1 10 8 13 800 Warehouse 2 12 15 9 1100 Warehouse...
SOLVE STEP BY STEP! 4. Consider the following LP: Minimize z = x; +3x2 - X3...
SOLVE STEP BY STEP!
4. Consider the following LP: Minimize z = x; +3x2 - X3 Subject to x + x2 + x2 > 3 -x + 2xz > 2 -x + 3x2 + x3 34 X1 X2,43 20 (a) Using the two-phase method, find the optimal solution to the primal problem above. (b) Write directly the dual of the primal problem, without using the method of transformation. (c) Determine the optimal values of the dual variables from the optimal...
3. The demand and supply for hospital care are given by the equations Q = 400...
3. The demand and supply for hospital care are given by the equations Q = 400 – P and Q = 80 + 3P, respectively. A. Solve for the equilibrium quantity and price. (5 pts). B. Now suppose that patients have insurance so that they only pay 20% of the price for hospital care. Solve for the new equilibrium quantity and price. (5 pts) 4. Consider the following demand and supply data Price Demand Supply 0 200 0 1 ...
(a) A retail chain has 3 distribution centers to serve 4 regions to meet the demand....
(a) A retail chain has 3 distribution centers to serve 4 regions to meet the demand. The transportation cost between the distribution centers and the regions is given in the following table. Unit Transportation Cost for Regions 2 3 4 1 А 12 15 13 11 Distribution B 8 16 12 10 Center C 9 17 11 13 The demand is expected to be 100, 90, 110, and 120 units in regions 1, 2, 3, and 4 respectively. The distribution...
TechWidget Incorporated maintains three warehouses located across the United States in order to service to four...
TechWidget Incorporated maintains three warehouses located across the United States in order to service to four customers. Warehouse has a supply of 35 units, warehouse 2 has a supply of 50 units, and warehouse 3 has a supply of 40 units. Customer 1 has a demand of 45 units, customer 2 has a demand of 20 units, customer 3 has a demand of 30 units, and customer 4 has a demand of 30 units. Provided below is a balance transportation...
11) c) Consider the following network diagram of a supply system, where the numbers associated with...
11) c) Consider the following network diagram of a supply system, where the numbers associated with the arrows represent unit shipping costs (from factories to warehouses). Our goal is to minimize the total shipping cost. Using Vogel's approximation method, find a Basic Feasible Solution to the problem and find the corresponding shipping cost. DEMAND FACTERIES WARENOUSES CAPAEITY 20 5 1-4 15 20 2 13 20 10 3
11) c) Consider the following network diagram of a supply system, where the...
Question 4 (20 marks) Let N be the network below, where ax and y are the source and sink respectively, and the arc S capacities are shown next to each arc. An initial flow of this network is given in parentheses 3(0) 6(0) 5(0) 4(0) 3(1) 2(0) X 2(1) 2(0) 3(1), 5(1) 4(0) 2(2) 2.5(1) V Starting from the given flow, use the labelling algorithm to find a maximum flow in N. Show every stage of the algorithm. State the...
4. Given a network of 8 nodes and the distance between each node as shown in Figure 1: 4 1 7 0 4 4 6 6 Figure 1: Network graph of 8 nodes a) Find the shortest path tree of node 1 to all the other nodes (node 0, 2, 3, 4, 5, 6 and 7) using Dijkstra's algorithm. b) Design the Matlab code to implement Dijkstra's algorithm
4. Given a network of 8 nodes and the distance between each...
A network map is given in the Excel file. a) Use the table in
the Excel file to find the fastest route from point A to point H.
For full credit, you must include the completed table in your
answer and show all possible solved and unsolved nodes in each step
until you solve for point H. b) What nodes do you pass through
along the fastest route from A to point H?
1 Problem 2 Network Map (all node...
SOLVE STEP BY STEP!
4. Consider the following LP: Minimize z = x; +3x2 - X3 Subject to x + x2 + x2 > 3 -x + 2xz > 2 -x + 3x2 + x3 34 X1 X2,43 20 (a) Using the two-phase method, find the optimal solution to the primal problem above. (b) Write directly the dual of the primal problem, without using the method of transformation. (c) Determine the optimal values of the dual variables from the optimal...
(a) A retail chain has 3 distribution centers to serve 4 regions to meet the demand. The transportation cost between the distribution centers and the regions is given in the following table. Unit Transportation Cost for Regions 2 3 4 1 А 12 15 13 11 Distribution B 8 16 12 10 Center C 9 17 11 13 The demand is expected to be 100, 90, 110, and 120 units in regions 1, 2, 3, and 4 respectively. The distribution...
TechWidget Incorporated maintains three warehouses located across the United States in order to service to four customers. Warehouse has a supply of 35 units, warehouse 2 has a supply of 50 units, and warehouse 3 has a supply of 40 units. Customer 1 has a demand of 45 units, customer 2 has a demand of 20 units, customer 3 has a demand of 30 units, and customer 4 has a demand of 30 units. Provided below is a balance transportation...
11) c) Consider the following network diagram of a supply system, where the numbers associated with the arrows represent unit shipping costs (from factories to warehouses). Our goal is to minimize the total shipping cost. Using Vogel's approximation method, find a Basic Feasible Solution to the problem and find the corresponding shipping cost. DEMAND FACTERIES WARENOUSES CAPAEITY 20 5 1-4 15 20 2 13 20 10 3
11) c) Consider the following network diagram of a supply system, where the...
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