(15 points total) A professor has been contacted by four not-for-profit agencies that are willing to work with student consulting teams. The agencies need help with budgeting, information technology (IT), coordinating volunteers, and forecasting. Although each of the four student teams could work with any of the agencies, the professor feels that there is a difference in the amount of time it would take each group to solve each problem. The professor's estimate of the time, in days, is given in the table below. Problem Solving Estimates Projects Budgeting Team Volunteers Forecasting 38 a. (2 points) To determine optimal assignment of teams to projects using a mathematical model, how many variables and how many constraints are required? b. (3 points) Formulate an appropriate objective function for this problem. Don't forget to define variables. c. (4 points) Formulate constraints which ensure that each team is assigned to exactly one project. d. (4 points) Formulate constraints which ensure that each project is allocated to exactly one team. e. (2 points) An optimal assignment of teams to projects is shown in the following output screenshot from the Assignment module of POM-QM software. Interpret the solutions and state which team is assigned to which project. What is the total duration of this optimal assignment? Volunteers Forecasting o Assignment Results (untitled) Solution Optimal solution value = 131 Team A Team B Team C Team D Budgeting 32 38 Assign 41 45 IT 35 40 42 Assign 45 15 Assign 18 Assign 27 35 25 38 30 42