To be completed using networks and graphs.

1. Prior to the beginning of school, a huge task occurs at almost every school in the nationcleaning the floors! Whether it be waxing, steam cleaning, or mopping, it is critical that the floors be ready for the first day of school. Your task is to design the plan for this cleaning project. Draw a graph of the hallways in your school or portion of your school (at least six edges). Assign weights to each edge according to the width and length of the corresponding hallway and how long it will take to complete that edge or hallway. Design a path through your school or portion of your school and determine the total number of hours required to complete the cleaning of the floors. 2. Describe a situation (other than travel) that requires a Hamiltonian circuit exist, but not an Euler circuit. Include either a diagram and graph or similar diagrams that show the connection of the graph to the real situation. Provide any details necessary to connect to the real-world application of this learning. 3. Construct a map that needs five colors. What is the largest number of colors required to color any map that keeps adjacent regions separate? Justify your response