IEOR 160 – Final Practice Questions Solution
Fall 2009
Problem 1
Three cities are located at the vertices of an equilateral triangle.
(That is, the distance
between any two cities is the same as the distance between any two other cities.)
An airport is to
be built at a location that minimizes the total (straightline) distance from the airport to the three
cities.
Clearly define the variables needed for this problem and formulate the objective function.
You need not solve the problem.
Solution
Assume on the axes of coordinate, the three cities lie in (0, 0), (0, a), (a/2, 3
1/2
a/2).
Suppose we build the airport at (x, y). Then we can formulate the problem into
Min (x
2
+y
2
)+(x
2
+(ya)
2
)+((xa/2)
2
+(y3
1/2
a/2)
2
)
Problem 2
Consider the following project data:
Activity
Predecesso
rs
Duration
(days)
A
 
4
B
 
5
C
A
16
D
B
11
E
A, B
17
F
D, E
7
a.
In the space below, draw the project network with
activities on nodes
.
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Compute each activity's EST (earliest starting time), LST (latest starting time) and slack.
Write your answers in the table below.
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 Spring '07
 HOCHBAUM
 Graph Theory, Shortest path problem, earliest completion time

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