Use the map to create a graph where vertices represent street intersections and edges represent streets. Define c(u,v) = 1 for all edges (u,v). Since a street can be traversed, start off by creating a directed edge in each direction, then make the transformation to a flow problem with no antiparallel edges as described in the section. Make the home the source and the school the sink. If there exist at least two distinct paths from source to sink then the flow will be at least 2 because we could assign f(u,v) = 1 for each of those edges. However, if there is at most one distinct path from source to sink then there must exist a bridge edge (u, v) whose removal would disconnect s from t. Since c(u, v) = 1, the flow into u is at most 1. We may …show more content…
Exercise 26.2-10
Suppose we already have a maximum flow f. Consider a new graph G where we set the capacity of edge (u, v) to f (u, v). Run Ford-Fulkerson, with the mod- ification that we remove an edge if its flow reaches its capacity. In other words, if f(u,v) = c(u,v) then there should be no reverse edge appearing in residual network. This will still produce correct output in our case because we never exceed the actual maximum flow through an edge, so it is never advantageous to cancel flow. The augmenting paths chosen in this modified version of Ford- Fulkerson are precisely the ones we want. There are at most |E| because every augmenting path produces at least one edge whose flow is equal to its capacity, which we set to be the actual flow for the edge in a maximum flow, and our modification prevents us from ever destroying this progress.
Problem 26-5
a. Since the capacity of a cut is the sum of the capacity of the edges going from a vertex on one side to a vertex on the other, it is less than or equal to the sum of the capacities of all of the edges. Since each of the edges has a capacity that is ≤ C, if we were to replace the capacity of each edge with C, we would only be potentially increasing the sum of the capacities of all the edges. After so changing the capacities of the edges, the sum of the capacities of all the edges is equal to C|E|, potentially an overestimate of the original capacity of any cut, and so of the minimum cut.
b.
The increasing number of Trinity’s student and the construction of aquatic centre have generated the major traffic issue within neighbourhood. The traffic report commissioned by the school seems to ignore the traffic problems at the school’s gate and car park entrance. The line of sight for drivers/motorist and pedestrian is impeded at each of the intersection close to the school. The frequently jammed at
This critique focuses on a graph published in the New York Times on April 29, 2016 at http://www.nytimes.com/interactive/2016/04/29/upshot/money-race-and-success-how-your-school-district-compares.html The graph is interesting as it addresses a critical issue that impacts the social, political and economic trends in the US. In particular, Rich, Cox and Bloch use a scatterplot to show the disparities in education attainment for students of different races and socioeconomic statuses. The scatterplot is unique as it mainly utilizes categorical data. In this case, there are three categorical variables, including the socioeconomic status (poorer and richer), race (white students, Hispanic, and black), and grade
(3 marks) c) Determine the optimal number of bus and train travelers. (2 marks) d) Say a train strike significantly reduced the number of trains available. By how much would the train capacity constraint have to fall for the optimal solution to be altered? (2 marks)
The company can afford to invest more fixed costs and variable costs (shifting assets from “A” to “C”) for additional “C” capacity thereby maximizing capacity utilization.
This is a picture of my BIC card and is what I get as a Medi-Cal recipient, and the other picture is my new insurance card. I chose this picture for government health programs because the department of Health and Human Services are where they provide Medicare and Medicaid. The department of Health Care Services is where they administer Medi-Cal, which is what I have. It is the nations largest Medicaid program and many Californians have it. It pays for almost half of all births in California, and a little more than half of all the revenues in California hospitals. Medi-Cal, which is what I have offers essential health benefits similar to what Covered California offer. When I visit the doctors or is taken to the emergency room, my expenses are
The message that I wish to convey to the parents of Hardin Elementary School here in Burkburnett Texas is what our PTO does for the teachers, students, and other parents. I want to make sure that parents know what we do, why we do it, and how they can help out as well. I feel as if most parents think that there is only a small group of parents that help and that is it, no one else can help. This is not the case. The PTO board may be a small group but PTO as a whole can include everyone. I wish to show the parents everything that we are involved in, in hopes of capturing their attention and getting them involved.
This is an anti-smoking advertisement geared towards parents of young children. The advertisement is overall plain and simple; it gets straight to the point when you look at it and utilizes a dark theme. This anti-smoking advertisement is trying to evoke a sense of “parental guilt” into parents who smoke. The way the advertisement is able to do this is through the use of an optical illusion, use of text and the use of negative space.
5. How would you go about deciding the appropriate batch size for the Stonehaven factory? What factors would you consider? How do they interrelate? (You may wish to do some calculations, but concentrate on thinking conceptually.)
15) In an unbalanced transportation problem where total supply exceeds total demand, the supply constraints will typically have "≥" inequalities.
In our urban and planning class, we discuss about the land use of specific areas and look over the official plan and the zoning-by-law. We select four bus stop where along the Gordon street and analysis each area behind the bus stops base on the city of Guelph documents. Gordon street is the busiest and main street in the Guelph city, and many bus lines should pass the Gordon street to the other places. The first bus stop we choose is Guelph Central Station which is the main transit station in the city, the second is Royal city park stop which represents entertainment and green space in downtown Guelph, the third stop closes to Campus Estates Plaza where is one of busy commercial land and the last one we choose is Solstice 1 Student
A) if the right-hand side value of the constraint increases by 1 unit, the objective function value will increase by 5 units
Humans have a fundamental need to belong and have social relationships, and therefore form groups to fulfill these basic human needs (Baumeister & Leary, 1995). The tendency to gravitate to similar individuals when building social ties is a well known feature of human behaviour, and is referred to as homophily (McPherson et al., 2001). It is possible that the tendency for homophily within populations, particularly the perception of physical similarity, influences seating preference more frequently than expected by chance in day-to-day social interactions (Mackinnon, Jordan, & Wilson, 2011). This increases the chances of interacting with similar others and decreases the chances of interacting with dissimilar others simply based on proximity.
Since the capacity is being expanded to increase production of Product C, it could be assumed that this increase should be allocated to this product. Production of Product A is to be scaled down, but its level of
Vertex claims the inventory costs of VLite are high, therefore tying practice is required to enhance sales of VLite. It is indisputable that the Commission recognizes pro-competitive effects of tying, such as lowering manufacturing or distribution costs by economies of scale, which is found to be important in this industry. According to para. 30 of the Guidance, Vertex has to prove that the tying is indispensible to achieve the same efficiencies. Also, following Hilti Vertex needs to show that it has taken other actions if possible in order to lower the inventory costs. Given such a high standard of proof, it is very likely that Vertex would be found violated the Article 102(d) by contractual tying.
In a larger city, the complexity of transportation increases manifolds because of the modes involved, the large number of origins and destinations, the amount and variety of traffic and the possibility of interference, particularly when this complexity is not managed effectively.