Scenario: The scholastic athletic league in which your school competes is exploring the possibility of adding women's field hockey and men's soccer to its varsity sports. To gauge interest and determine the "skill" level of potential participants, the league will be hosting a sports day that your AD has volunteered to organize. The AD has passed planning responsibilities to you. So far you have received commitments for $5$ soccer and $6$ field hockey "teams." Available facilities$/$equipment include two gymnasiums $($each dividable into two full sized basketball courts$),$ three playing fields $(120$x$80$yds$.,$ each lined for both sports$),$ six portable soccer goals, six portable field hockey goals, and $30$ orange rubber cones. All other playing equipment is the responsibility of each participating team. Additionally, two field hockey and three soccer officials will be present for the day's event.

$1.$ Solve the Problem: Develop a schedule that ensures all teams have an opportunity to compete equally and determines the best team in each sport. Schedule must identify team playing location, equipment movement$/$relocation$,$ contest duration, timekeeper$/$officials$.$ No playing area may be used for longer than a two$-$hour block of time for any one activity.

$2.$ Contingency: What adjustments in your schedule would you make if it started to rain heavily halfway through the event?