Consider the following order-requirement digraph which represents a job: prepari
ID: 3144102 • Letter: C
Question
Consider the following order-requirement digraph which represents a job: preparing a restaurant entree by executing eight inter-related tasks. In the graph, vertices represent the tasks and are labeled T_1 - T_8. For each of these tasks, the time in minutes required for a member of the kitchen staff to perform the task is given within the vertex. A directed edge between two vertices indicates that the task where the edge starts must be finished before the task where the edge ends can begin. Assume that tasks, once started, are not interrupted. 1. List all "left-to-right" paths contained in the digraph (i.e., restrict your list to those that start with T_1 or T_2 and end with T_7 or T_8). How many such paths are there? 2. Which is this job's critical path? 3. What is the length of this job's critical path? 4. If only one member of the kitchen staff is available to prepare the entree, how long will it take? 5. If only one member of the kitchen staff is available to prepare the entree, and if T_1 is started at 6: 30 pm, what's the earliest time that T_3 can be started? 6. If only one member of the kitchen staff is available to prepare the entree, and if T_1 is started at 6: 30 pm, what's the earliest time that T_4 can be started? 7. If two members of the kitchen staff are available to prepare the entree, what is the least amount of time it could possibly take? 8. If three members of the kitchen staff are available to prepare the entree, what is the least amount of time it could possibly take? 9. If two members of the kitchen staff are available to prepare the entree, and if T_1 and T_2 are started at 6: 30 pm, what's the earliest time that T_5 can be started?Explanation / Answer
1. a).T1,T3,T5,T7
b)T1,T3,T5,T8
c)T2,T3,T5,T7
d)T2,T3,T5,T8
e) T2,T4,T5,T7
f) T2,T4,T5,T8
g) T2,T4,T6,T8
h) T2,T4,T6,T7
2. T2,T3,T5,T8
3. 37
4. 29
5. 6:36
6. 6:58
7. 35
8. 32
9. 6:41