Network Flows Case Study
MTH/221

Network Flows Case Study
Example 1

Joe the plumber has completed a very unique set of plumbing connections to create a network allowing three gallons per minute at maximum flow. The above left diagram is the original pipe set with the allowed gallons throughput per minute. The above left diagram is the tree diagram displaying how the pressure amounts allotted allows for the pressure to reach the required three gallons. First, starting at s, four gallons per minute are released and split in half at point a, but as the top dark blue path to b allows for three gallons it was tested if three gallons were utilized through the top to either conclude if three gallons would reach the ending destination …show more content…
Example 3

At Major University the graders hired have specific courses they are capable of grading with amount wanted to grade as maximum. Meanwhile, Professor Johnson has the requirements of how many of each section must be graded and can use less than the maximum of the students’ requested maximum amount to complete the courses needed. There are several different ways to resolve this problem. Below is a diagram of all possibilities to fulfill the above requirements of courses while also not going over the maximum sections requested by the graders.

These solutions are color-coded based on the student graders and can only grade the sections they are approved to grade. The red numbers represent Student 1, green represents Student 2, and purple represents Student 3. C1, C2, C3, and C4 represent their respected course numbers. The solutions in the boxes are which specific course the student will grade in order to reach the requirements for the courses needing to be graded. The chart above the solutions represents how many sections each student will be completing in order to reach the total seven sections to be graded. If Professor Johnson was looking for the solution that had the amount of courses and variety at its peak then there is one solution that would fit the best. The best fit is the third listed on the left showing Student 1 grading two Course 1 and one Course 2, Student 2