No flow networks have an edge directly (back) from t to s.(a) Explain why such an edge is impossible.(b) Suppose such an edge did exist in a network. Explain (using augmenting paths) why anymaximum flow would avoid the direct back edge.

Introduction: In the context of flow networks, an augmenting path is a simple path from the source s…

Answered: No flow networks have an edge directly…

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter2: Systems Of Linear Equations

Section2.4: Applications

Problem 15EQ

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Redo Exercise 5, assuming that the house blend contains 300 grams of Colombian beans, 50 grams of Kenyan beans, and 150 grams of French roast beans and the gourmet blend contains 100 grams of Colombian beans, 350 grams of Kenyan beans, and 50 grams of French roast beans. This time the merchant has on hand 30 kilograms of Colombian beans, 15 kilograms of Kenyan beans, and 15 kilograms of French roast beans. Suppose one bag of the house blend produces a profit of $0.50, one bag of the special blend produces a profit of $1.50, and one bag of the gourmet blend produces a profit of $2.00. How many bags of each type should the merchant prepare if he wants to use up all of the beans and maximize his profit? What is the maximum profit?
23. Consider a simple economy with just two industries: farming and manufacturing. Farming consumes 1/2 of the food and 1/3 of the manufactured goods. Manufacturing consumes 1/2 of the food and 2/3 of the manufactured goods. Assuming the economy is closed and in equilibrium, find the relative outputs of the farming and manufacturing industries.
1) (a) Find the general pattern of the network drawn on the figure. (b) Assuming that the flow must be in the direction indicated, find the minimum flows in the branches denoted by x2, x3, x4, and x5.
2. The figure below represents the traffic entering and leaving a roundabout road junction in Continental Europe. Such roundabouts ensure the continuous smooth flow of traffic at road junctions. Construct a system of linear equations describing the flow of traffic along the various branches. Use these equations to determine the minimum flow possible along xị. What are the other flows at this time? Explain what happens to x7 traffic. It is not necessary to compute the reduced echelon form. Use the fact the traffic flow can't be negative. The traffic is measured in vehicles per hour (vph). 90 A 100 X3 X2 X1 155 130 120 110 X6 X7 X5 80 75

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No flow networks have an edge directly (back) from t to s. (a) Explain why such an edge is impossible. (b) Suppose such an edge did exist in a network. Explain (using augmenting paths) why any maximum flow would avoid the direct back edge.