Scheduling SOL: DM.1 Classwork Scheduling Class Project & Club Conflict Resolution (from powerpoint slide) Homework (day 55) CELEBRATE (from powerpoint slide)- graded!

Suggested Scheduling Steps: Draw a table Put an “X” in the box(es) if the student is involved in more than one project Make a vertex drawing (draw vertices where you have “x’s” Color the vertices The chromatic number tells you how many “days” are needed.

Scheduling Class Project Eight students in your class are working on six discrete math projects, but they are having a hard time arranging for times to meet. Each meeting will need a full 45-minute class period during seventh period on Monday, Tuesday, Wednesday, Thursday or Friday and you want to use as few class periods as necessary. Can you help them out by creating a conflict matrix? Note: This is similar to the map-coloring problem, excepts that you have to assign days to projects instead of colors to states. Projects Students Day Assigned Euler Paths & Circuits Sarita, Barbara, Ravi Linear Programming Sarita, Roberto Coloring Roberto, Maimuna Induction Maimuna, Boris, Christie Tiling Barbara, Boris, Jason Voting Ravi, Christie, Jason

Club Conflict Resolution A school has six clubs which each meet once a week afterschool. The presidents of the clubs have gotten together to decide which day each club should meet. It was observe that if a student belongs to two clubs, then those clubs cannot meet on the same day. Construct a conflict matrix. What is the fewest number of days needed for these clubs? Club Students Art Al, Bob, Charlie Boating Deb, Geoff, Hilda Calligraphy Al, Deb, Edna Dancing Edna, Fran, Jen Fencing Charlie, Ida, Ken Geography Hilda, Ida, Len History Fran, Geoff, Miguel

CELEBRATE NRHS Reunion 2016!!!! (this will be a grade) It’s your ten-year high school reunion and the following committees have been formed to help plan the celebration: Food, Invitations, Entertainment, Lodging, Decorations and Alumni Directory. Some people have signed up for more than one committee. For example, Sean has signed up for the Food committee and Entertainment committee meetings, we can’t schedule them at the same time. All of the committees and committee members are listed in the next slide. 1) Construct a conflict matrix. 2) What is the minimum number of times we can schedule meetings so that everyone will be able to be present at all of his/her meetings? 3) Which committees can met at the same time? 4) How are Planar Graphs and the Four Color Theorem related to this problem?

Food Invitations Entertainment Lodging Decorations Alumni Directory Rachel Katie Eric Jennifer Robert April Angie Gavin Kyle Amber Travis Zach Aubrey Dan Tosin Jason Sean Ryan Julie Anne Matt