UNSW Sydney
TRIMESTER 2 2020 EXAMINATIONS
ENGG1400: ENGINEERING INFRASTRUCTURE SYSTEMS


1. DATE AND TIME – Start at 2pm on 24 August 2020 (Sydney time); End at 4pm same day
2. READING TIME – 10 minutes
3. TOTAL NUMBER OF PROBLEMS – 3
4. TOTAL MARKS AVAILABLE – 100
5. MARKS AVAILABLE FOR EACH QUESTION ARE SHOWN IN THE EXAMINATION PAPER
6. THE ORDER OF CHOICES IN MULTIPLE CHOICE QUESTIONS IS AUTOMATICALLY SHUFFLED
IN MOODLE, HENCE THE ORDER OF CHOICES AS LISTED IN THIS DOCUMENT MAY NOT BE
THE SAME AS WHAT YOU SEE IN THE ONLINE QUIZ.

Note: this document is only a summary of the questions of the final
examination which is provided for convenience purposes.

All answers must be provided online by accessing the Moodle quiz activity
named “Final Examination”








Problem 1: Project Scheduling Problem (32 pts)
An engineering project is to be conducted. The following network diagram shows the
involved activity numbering and their duration in days (within parentheses).

1. Determine the earliest time to complete the project using the critical path method
(unit is not required). (8 pts)


2. How many critical paths do you find? (6 pts)


3. If you identify one critical path, how many activities are involved along this path?
If you identify more than one critical path, how many activities are involved along
the longest path (i.e. the path that has the greatest number of activities)? (6 pts)






4. Assuming that activities which are not on the critical path(s) start at their earliest
possible time, determine whether the following Gantt chart is correct or not. (6 pts)

a. True
b. False



5. Due to an unexpected incident, the duration of activity 14 has to be extended by 4
days. What is the new earliest completion time (no unit is required)? (6 pts)











Problem 2: Multiple Choice Questions (32 pts)
1. Consider the network below with nodes represented in red circles and links in black
lines. All links are bi-directional and have the same cost in both directions. The
number next to each link is the cost of this link.


Let node 0 be the source node. In which order are the nodes visited when
implementing Dijkstra's algorithm to this network? (8 pts)
a. 0, 1, 7, 6, 5, 2, 8, 3, 4
b. 0, 1, 7, 6, 2, 5, 8, 3, 4
c. 0, 1, 7, 6, 5, 2, 3, 8, 4























2. Consider the feasible region (in blue) of the linear program below:



If the x-axis represents variable x1 and the y-axis represents variable x2, and if the
objective function is: maximise 25*x1 + 25*x2, what is the optimal solution of this
problem? (6 pts)
a. x1=50, x2=0
b. x1=0, x2 = 55
c. x1=20, x2=45

3. Select the statements which are true. (6 pts)
Select one or more:
a. In an integer program, the number of solutions is always lesser or equal than the
number of constraints.
b. In an integer program, relaxing the the integrality restriction on the decision
variables does not always change the optimal solution.
c. In an integer program, the number of solutions is always greater than the number of
constraints.
d. In an integer program, if a solution exists, the optimal solution cannot have
fractional values.



4. Consider the optimisation problem below:

What is the number of feasible solutions of this optimisation problem? (6 pts)
a. 6
b. 8
c. Infinite


5. Consider the list of four items below with their given value and weight.

These items are non-divisible and only one copy of each item is available, that is item
A is only available once, item B is only available once, etc.
Two knapsacks are available to pack the items: a large knapsack of capacity 40 and a
small knapsack of capacity 30. Items cannot be divided across the two knapsacks.
What is the maximum value that can be obtained in this multiple knapsack problem?
(6 pts)
a. 15
b. 18
c. 17

Problem 3: Food supply chain design (36 pts)
A regulator in the food distribution industry is in charge of designing the supply chain from
producers (growers, farmers) to retailers (local fresh produce stores). The food supply chain
affects the revenue and the costs of producers by influencing the travel and storage costs of
goods as well as their selling price. One of the regulator’s goal is to improve the welfare of
producers so that they are incentivized to use the regulator’s supply chain. To reduce
shipments costs, hubs can be setup consolidate producers’ goods and facilitate the
distribution to retailers. Hubs are typically profitable when they are operating near capacity,
otherwise they may be too costly to operate. Hence, the regulator would also like to reduce
the supply chain operating costs and would like to take into account the carbon footprint of
the supply chain.


1. List 3 factors that you believe should be taken into consideration when calculating
the welfare of producers. (6 pts)
Factor 1:
Factor 2:
Factor 3:

2. List 3 factors that you believe are critical to decide whether or not to setup a hub at
certain location. (6 pts)
Factor 1:
Factor 2:
Factor 3:


3. What could be the variables of the regulator’s optimisation problem? (8 pts)



4. What could be the constraints of the regulator’s optimisation problem? (8 pts)



5. What could be the objective function(s) of the regulator’s optimisation problem? (8
pts)