7. For this question, consider the Gina 3000 project described in Examples 14.1 and 14.2 of the textbook. a. (***) Consider Table 14.4 and Figure 14.5. Every week the project continues costs the Courter Corporation an additional $5,000 in lost profits. The quality control manager says she can crash activity H from 3 weeks down to 2 weeks by working overtime. Doing so would cost an additional $2,000. Should Courter do it? b. (***) Writing up the product specifications (activity F) is taking longer than expected. Assuming that no other activities have been delayed or crashed, how many weeks can activity F be delayed without delaying the entire project? EXAMPLE 14.2 Network Diagram for the Gina3000 Project Courter Corporation decides to follow the six steps outlined above to create a network dia- gram of the Gina3000 project. Step 1. Identify each unique activity in a project by a capital letter that corresponds only to that activity. This has already been done in Table 14.2. Step 2. Represent each activity in the project by a node that shows the estimated length. To illustrate, "Customer uses and approves prototypes" (activity C) is estimated to take 3 weeks. Courter represents this as follows: Step 3. If an activity has an immediate predecessor, show that relationship by connecting the two activities with an arrow. Activity A immediately precedes activity C. This is shown as follows: The same logic is used to link all the activities in the project. The result is the AON network diagram for the Gina3000 project shown in Figure 14.4. Note that there is one ar- row for each predecessor relationship listed in Table 14.2. B, 3 D, 5 H, 3 1, 2 1,3 FIGURE 14.4 AON Network Diagram for the Gina3000 Project Now consider the fact that even though activity A is not listed as an immediate predeces- sor for any activity except C, it must still be completed before all other activities, except for B. That is, all the activities except B are on a network path in which activity A is the first activity that must be completed. One path through the network is the sequence A-C-F-G-J. This path implies that A must be completed before C, C before F, and so on. Paths are the key to understanding the relationship between activities and determining the length of a project. There are a total of eight different paths in this network. Can you find all of them? EXAMPLE 14.1 Gantt Chart for the Gina3000 Project Courter Corporation makes high-end speakers that are used with home entertainment sys- tems. Courter has designed a new speaker, the Gina3000, which is louder and more reliable than Courter's earlier model. Before Courter goes any further, however, it wants to give its customers the home entertainment system manufacturers-a chance to test and critique the Gina3000. Management has outlined 10 activities that must be completed before the Gina 3000 speakers can be released for regular production. These 10 activities are listed in Table 14.2. There are a couple of interesting things to note about Table 14.2. First, some activities, such as A (Legal department approves prototype use) and B (R&D builds prototype speak- ers) can occur simultaneously. Courter Corporation should consider this when planning the expected time for the project's completion. Second, some activities have predecessors that must be completed beforehand. Take activity H, for example. Obviously, one can't test sample speakers before they have been made (activity E). Likewise, activity E can't be com- pleted until the new equipment has been ordered and installed (activity D). TABLE 14.4 Results of Forward and Backward Passes on the Gina3000 Project DURATION ACTIVITY (WEEKS) PREDECESSORS ES EF LF A 2 None 0 2 3 B None 0 3 3 A, B 3 6 6 6 11 13 C 9 E, F E E G, H, I AGILA G+ 235NM M M M N 3 3 3 2 11 6 13 13 13 16 16 16 899 41036 LS 11 10 13 13 13 16 336 *Critical activity. A, 2 C, 3 F, 3 G, 3 B, 3 D, 5 E, 2 H, 3 1, 2 1,3 FIGURE 14.5 AON Network Diagram for the Gina3000 Project (critical activities and paths marked in red) 11 13 13 16 16 16 18