Each spring the Tech Student Government Association (SGA) organizes an event called "Give Back Weekends." The SGA solicits student teams to work on projects for residents in the university community on four consecutive Saturdays in April. The coed student teams generally are made up of three to five students from various dormitory groups, fraternities, sororities, and student clubs and organizations. The SGA invites projects from the residents by sending out a form during the winter enclosed in the residents' town utilities bills and through newspaper ads and its Internet site. The residents complete the form that briefly describes the work at their home that they want done, which is primarily yard cleanup work, plus odd jobs like window washing, painting, and hauling away unwanted items to Goodwill or the dump. Once the forms are submitted the SGA event coordinators visit the homes with the team leaders to assess the work involved and the team leaders provide an estimate of the time that will be required for their team to complete the project. The time to complete a project 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, since 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 projects for the first Saturday in the event:

The SGA's primary objective is to complete all 12 projects,
if possible. Each team can work on multiple projects
but cannot work more than 8 hours on Saturday. The SGA
wants each team to be involved by working on at least one
project.
a. Determine the optimal assignment of teams to projects that will maximize the number of projects completed.
b. Determine the assignment of teams to projects if the SGA wants to complete all 12 projects 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?

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