Each spring Denizli University$$s Departments of Health, Culture and Sports $($DHCS$)$ organizes an event called $$Spring Fest.$$ The DHCS solicits student teams to work for arranged activities on four consecutive Saturdays in April. The coed student teams generally are made up of three to five students from various student clubs.

The time to complete an activity will vary between the teams because of the different number of team members, the skills of the team, and the physical make$-$up of the team because most projects involve manual labor. Following are the time estimates $($in hours$)$ submitted by the six teams available to work on the projects for the $12$ activities for the first Saturday in the event:

The DHCS$$s primary objective is to complete all $12$ activities, if possible. Each team can work on multiple projects but cannot work more than $8$ hours on Saturday. The DHCS wants each team to be involved by working on at least one activity.

Questions $(50$ pts each$)$

A$.$ Determine the optimal assignment of teams to activities that will maximize the number of activities completed.

B$.$ Determine the assignment of teams to activities if the DHCS wants to complete all $12$ activities while minimizing the total time required for all six teams. What, if any, is the difference between the two solutions. What is the average time per team?$\backslash$table$[[,$Jobs$],[$Team$,1,2,3,4,5,6,7,8,9,10,11,12,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,],[1,5,1\mathrm{.}5,6,4,3\mathrm{.}5,3,6,1\mathrm{.}5,5,1,3,3\mathrm{.}5,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,],[2,4,2,5,5,3,3,5\mathrm{.}5,2,4,1\mathrm{.}5,4,2\mathrm{.}5,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,],[3,5,1\mathrm{.}5,6\mathrm{.}5,3\mathrm{.}5,2\mathrm{.}5,4,4\mathrm{.}5,3,3\mathrm{.}5,1,3\mathrm{.}5,4,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,],[4,3\mathrm{.}5,2,5\mathrm{.}5,4,3\mathrm{.}5,2\mathrm{.}5,5,2\mathrm{.}5,4,1\mathrm{.}5,2\mathrm{.}5,4,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,],[5,3\mathrm{.}5,3,5,3,2,4,5,2,5,2,4,3,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,],[6,4,2\mathrm{.}5,6,5,3,3,6,3,3,2,3,3\mathrm{.}5,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,]]$