Question: A decision needs to be made about the best way to assign each of the four teams to each of the four projects. An estimate

A decision needs to be made about the best way to

A decision needs to be made about the best way to assign each of the four teams to each of the four projects. An estimate of the amount of time each team would take, in days, to complete each project if that team were assigned to it. The manager wants to keep project completion times as low as possible. Team A B D Budgeting 36 39 43 42 Projects Information Volunteers 32 19 44 18 47 23 41 Forecasting 28 32 39 31 41 1) Write the linear programming objective function and constraints for the problem above. Use the following variables ... X11 = Team A assigned to Budgeting ... X12 = Team A assigned to Information ... X13 = Team A assigned to Volunteers ... X14 = Team A assigned to Forecasting ... X21 = Team B assigned to Budgeting ... X22 = Team B assigned to Information ... X23 = Team B assigned to Volunteers ... and so on until you get to X44 = Team D assigned to Forecasting. Looking at the output below for the above problem, answer the following questions ... What project will team C be assigned to? Which team should be assigned to Budgeting? How many days in total for all the teams to complete all four projects? OPTIMAL SOLUTION Objective Function Value = 129.000 Variable Value Reduced Costs X11 X12 X13 X14 X21 X22 X23 X24 X31 0.000 1.000 0.000 0.000 0.000 0.000 0.000 1.000 0.000 2.000 0.000 5.000 0.000 1.000 8.000 0.000 0.000 0.000 X32 X33 X34 X41 X42 X43 X44 0.000 1.000 0.000 1.000 0.000 0.000 0.000 6.000 0.000 2.000 0.000 1.000 9.000 5.000 Constraint Slack/Surplus Dual Prices 1 2 3 4 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 9.000 5.000 0.000 1.000 -43.000 -41.000 -23.000 -37.000 5 6 7 8 OBJECTIVE COEFFICIENT RANGES Variable Lower Limit Current Value Upper Limit X11 X12 X13 X14 X21 X22 X23 X24 X31 X32 X33 34.000 No Lower Limit 14.000 27.000 38.000 36.000 17.000 30.000 42.000 41.000 22.000 36.000 No Upper Limit 32.000 33.000 19.000 No Upper Limit 28.000 30.000 39.000 No Upper Limit 44.000 No Upper Limit 18.000 19.000 32.000 33.000 43.000 44.000 47.000 No Upper Limit 23.000 24.000 X34 37.000 39.000 No Upper Limit X41 No Lower Limit 42.000 43.000 X42 40.000 41.000 No Upper Limit X43 22.000 31.000 No Upper Limit X44 36.000 41.000 No Upper Limit RIGHT HAND SIDE RANGES Constraint Lower Limit Current Value Upper Limit 1 2 3 4 1.000 1.000 1.000 1.000 1.000 0.000 0.000 0.000 1.000 2.000 1.000 2.000 1.000 No Upper Limit 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 5 6 7 8

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