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5. Imagine that you are in charge of planning a short course for executives wishing to upgrade their Operations Research skills. The following list of activities is involved: Cost Per ImmediateNormal DescriptionPredecessors (days) Crash Time (days)Reduction Day of Time Activity A Develop course outline 4 S50 Arrange speakers $100 Identify potential locations $150 Choose location 4 $150 Arrange travel for B, D speakers Final confirmation of $200 eakers Advertise course B, D Take rescrvations Arrange welcome party F, H $100 i) Using the list of activities, their precedence relationships, and their normal durations, draw a suitable project network. i) Determine the early event time, the late event time, and the total float for each activity iii) Identify the critical activities and then determine the critical path. iv) Using the additional information concerning crash time and cost per day of time reduction write down an LP program that could be used to determine the minimum cost of crashing the project so that it could be completed in 24 days. NOTE: The crash time is the absolute shortest time in which an activity can be completed.

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HIdentiy the ateonative paths and cait ca f parhs and coitical pth coittcal patn i the path of longest durahon n the netiwork A- B-6 H-I 28 cíticalmth 0 19 O 27 A-B-E F-I C-D-4-H-I C-D--F-I Nomal Time28 day s り!inen par goa mto shost en fhe paced to 24 day r at minimum cost is fotlowing Let Va Xb, xc Xi ke the number of dayc thcat vespective activity is Coashed by, and A,B,, epaeent the eavliest finish time of despecive activity

工く上24 xgFo All vcsiableso colu tion of the LP using LINDO following

Lingo 17.0 Solution Report Lingol File Edit Solver Window Help 0133 Solution Report . Lingo! Global optimal solution found Objective value: Infeasibilities: Total solver iterations: Elapsed runtime seconds: Lindo Model Lingol 450.0000 0.000000 0.24 B A + Xb >-5 Model Class: LP Total variables: Nonlinear variables: Integer variables: 16 Total constraints: Nonlinear constraints: 21 Total nonzeros: Nonlinear nonzeros: 45 24 Ха-2 Variable XA хв XC XD Value 1.000000 0.000000 0.000000 0.000000 0.000000 2.000000 1.000000 3.000000 8.000000 4 . 000000 8.000000 10.00000 0.000000 14.00000 15.00000 0.000000 21.00000 24.00000 Reduced Cost 0.000000 50.00000 0.000000 0.000000 200.0000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 Xe-0 ХН XI XE XG For Help, press F1 Ln 33, Col 21 5:51 am

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