Question: Consider the filming of the scene described in Problem. Based on past experience, the director is not very confident about the time estimates for some of the activities. The director's estimates for the minimum, most likely, and maximum times for these activities are

Activity                a              m                 b

F                       2            3             12

I                        1            2              8

J                        3            4             10

K                            1            2              7

a. Including these PERT time estimates, how long is the filming expected to take?

b. What is the probability that the number of days required to complete the filming of the scene is at least 30 percent larger than the answer you found in part (a)?

c. For how many days should the director plan in order to be 95 percent confident that the filming of the scene is completed?

Problem: A scene is being shot for a film. A total of 11 distinct activities have been identified for the filming. First, the script must be verified for continuity, the set erected and decorated, and the makeup applied to the actors. After the set is completed, the lighting is set in place. After the makeup is applied, the actors get into costume. When these five activities are completed, the first rehearsal of the scene commences, which is followed by the second scene rehearsal with the cameraperson. While the rehearsals are going on, verifications of the audio and the video equipment are made. After both rehearsals and verifications are completed, the scene is shot. Afterward, it is viewed by the director to determine if it needs to be reshot. The list of the activities and the activity times is

a. Develop a network for the filming of the scene.

b. Compute the earliest and the latest finishing and starting times for each of the activities, and identify the critical path.

c. Draw the Gantt chart for this project. Assume that activities with slack are scheduled so that there is equal slack before and after the activities.

d. Suppose that the video verification (G) shows that the equipment is faulty. Four additional days are required to obtain and test new equipment. How much of a delay in the total time required to film the project will result?

e. One of the costumes is damaged as it is being fitted (activity E). How much extra time is available for repair without delaying the project?

f. What kind of delays can you envision as a result of the uncertainty in the time of activity K?

g. Solve this problem by linear programming.