Math + Optimization

Consider the following project with time measured in days and costs in thousand dollars. The minimum time can be achieved at maximum cost by obtaining additional resources. TI Normal Minimum Normal Maximum Activity Predecessors Time Time Cost Cost A None 14 12 15 17.5 B 14 11 55 64 B 8 5 50 75 NONE 12 9 40 50 E B,D 18 16 50 65 F CE 20 16 40 55 G 14 10 55 70 F G 21 19 25 65 10 8 25 32 J 20 10 50 120 9 6 25 40 L 15 10 10 40 L-IMO > WI-3x a) Using the normal times, formulate a linear program to determine a start time for each activity that would minimize the project's total duration. Constrain all start times to be unrestricted in sign except for the dummy START activity which should have a nonnegative start time. Solve the created model using excel solver b) Create the Activity-On-Nodes Network for this project. c) Using exhaustive enumeration and normal times determine all critical paths for this project. Consider the following project with time measured in days and costs in thousand dollars. The minimum time can be achieved at maximum cost by obtaining additional resources. TI Normal Minimum Normal Maximum Activity Predecessors Time Time Cost Cost A None 14 12 15 17.5 B 14 11 55 64 B 8 5 50 75 NONE 12 9 40 50 E B,D 18 16 50 65 F CE 20 16 40 55 G 14 10 55 70 F G 21 19 25 65 10 8 25 32 J 20 10 50 120 9 6 25 40 L 15 10 10 40 L-IMO > WI-3x a) Using the normal times, formulate a linear program to determine a start time for each activity that would minimize the project's total duration. Constrain all start times to be unrestricted in sign except for the dummy START activity which should have a nonnegative start time. Solve the created model using excel solver b) Create the Activity-On-Nodes Network for this project. c) Using exhaustive enumeration and normal times determine all critical paths for this project