OR 7205  Fall 2023
Homework 1
Due: Thursday, 21 September 2023, 11:59 PM
Instructions:
•
This assignment is to be done individually  you must do your own work.
Preliminary Questions (5 Points)
1.
(3 Points)
Introduce yourself in one paragraph.
Tell us about your background,
degrees you have, universities you earned those degrees from, the relevant courses you
have passed before, the year you were admitted at NU, and anything else you may
think might be useful we know you better.
2.
(2 Points)
Read the syllabus and confirm you have read it completely.
Part I. Introduction to Deterministic OR (47 Points)
1.
(9 Points)
Read the application vignettes on page 25, 54, and 59 of your textbook
and summarize them here.
2.
(6 Points)
Write the parameters and coefficients of the following LP in matrix format.
(
P
1)
maximize
x
1
,x
2
,x
3
5
x
1
+ 3
x
2
+ 2
x
3
subject to:
2
x
1
+
x
2
+ 4
x
3
≤
4
,

x
1
+
x
2

2
x
3
≤
1
,
x
1
+ 3
x
2
+
x
3
≤
2
,
x
1
, x
2
, x
3
≥
0
.
3.
(18 Points)
For the following mathematical programming problem identify the LP
assumptions that are violated in each line. Justify your answers.
(
P
2)
minimize
x
1
,x
2
,x
3
2
x
1
+ 3
x
1
x
2
+ 3
x
3
subject to:
(1)

4
x
1
+
x
2
+ 5
x
2
3
≥
7
,
(2)
x
1

x
2
+ 2
x
3
≤
p ,
p
∈ {
0
.
4
,
0
.
6
}
(3)
x
1
/x
3
+ 3
x
2
+
√
x
3
≤
3
,
(4)
x
1
≤
0
,
(5)
x
2
≥
0
,
integer
(6)
x
3
∈
R
.
(7)