题目
A project is modelled by the activity network shown in Figure 3. The activities are represented by the arcs. The number in brackets on each arc gives the time, in days, to complete the activity. Each activity requires exactly one worker. The project is to be completed in the shortest possible time.
(a) Explain the purpose of the dummy between event 10 and event 11.
(b) Complete Diagram 1 in the answer book to show the early event times and the late event times.
(c) State the critical activities.
(d) Calculate the maximum number of days by which activity K could be delayed without lengthening the completion time of the project. You must make the numbers used in your calculation clear.
(e) Draw a Gantt (cascade) chart on the grid in the answer book.
(f) Use the Gantt chart to determine a lower bound for the minimum number of workers required to complete the project in the minimum time. You must make specific reference to the number of workers, activities and times.
题目中文翻译
一个项目由图 3 所示的活动网络建模。活动由弧表示。每条弧上括号内的数字是完成活动所需的时间（单位：天）。每个活动恰好需要一名工人。项目应在最短时间内完成。
(a) 解释事件 10 和事件 11 之间虚活动的目的。
(b) 在答案本中完成图 1，显示最早事件时间和最晚事件时间。
(c) 说明关键活动。
(d) 计算活动 K 在不延长项目完成时间的情况下可以延迟的最大天数。必须清楚说明计算中使用的数字。
(e) 在答案本中的网格上绘制甘特图（级联图）。
(f) 使用甘特图确定在最短时间内完成项目所需最少工人数量的下界。必须具体说明工人数量、活动和时间。