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 hours, to complete the corresponding activity. Each activity requires one worker. The project is to be completed in the shortest possible time using as few workers as possible.
(a) Complete Diagram 1 in the answer book to show the early event times and the late event times.
(b) Calculate the total float for activity D. You must make the numbers used in your calculation clear.
(c) Calculate a lower bound for the minimum number of workers required to complete the project in the shortest possible time. You must show your working.
(d) Draw a cascade chart for this project on Grid 1 in the answer book.
(e) Use your cascade chart to determine the minimum number of workers needed to complete the project in the shortest possible time. You must make specific reference to time and activities. (You do not need to provide a schedule of the activities.)
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相应活动所需的时间（单位：小时）。每项活动需要一名工人。项目应在使用尽可能少的工人的情况下在最短时间内完成。
(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 D 的总时差。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最小工人数量的下界。必须展示计算过程。
(d) 在答案本的网格 1 上画出此项目的级联图。
(e) 使用级联图确定在最短时间内完成项目所需的最小工人数量。必须具体说明时间和活动。（不需要提供活动时间表。）