题目
A project is modelled by the activity network shown in Figure 1. 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) Complete Diagram 1 in the answer book to show the early event times and the late event times.
(b) Calculate the maximum number of days by which activity H could be delayed without lengthening the completion time of the project. You must make the numbers used in your calculation clear.
(c) Calculate a lower bound for the number of workers needed to complete the project in the minimum time. You must show your working.
(d) 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.
题目中文翻译
一个项目由图 1 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) 计算活动 H 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。
(c) 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。
(d) 在答案本的网格 1 上安排活动，使用最少数量的工人，使项目在最短时间内完成。