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 corresponding activity. Each activity requires exactly one worker. The project is to be completed in the shortest possible time.
(a) Complete Diagram 1 in the answer book to show the early event times and the late event times.
(b) Calculate a lower bound for the number of workers needed to complete the project in the minimum time. You must show your working.
(c) Schedule the activities on Grid 1 in the answer book using the minimum number of workers so that the project is completed in the minimum time.
Additional resources become available, which can shorten the duration of one of activities D, G or P by one day.
(d) Determine which of these three activities should be shortened to allow the project to be completed in the minimum time. You must give reasons for your answer.
题目中文翻译
一个项目由图 3 所示的活动网络模拟。活动由弧表示。每条弧上的括号内的数字表示完成相应活动所需的时间（单位：天）。每项活动恰好需要一名工人。项目应在最短时间内完成。
(a) 在答案本中完成图 1，显示最早事件时间和最迟事件时间。
(b) 计算在最短时间内完成项目所需的工人数量的下界。必须展示计算过程。
(c) 在答案本的网格 1 上使用最少数量的工人安排活动，使项目在最短时间内完成。
额外资源变得可用，可以将活动 D、G 或 P 中的一个的持续时间缩短一天。
(d) 确定应缩短这三个活动中的哪一个以允许项目在最短时间内完成。必须给出理由。