INSY 7420 Linear Programming & Network Flows
Practice Problems to Accompany Slide Set #1
These problems will not be graded
SOLUTION KEY
1. (from BJS) Consider the problem: Minimize cx subject to Ax b, x 0.
Consider that we started with the following probl

INSY 7420
Linear Programming
Homework 1
Due date: Thursday February 4th at the end of the class
Directions: a hard-copy of the report is due at the end of the class on Thursday February 4th.
For the problems that require you to come up with a problem form

INSY 7420 Linear Programming & Network Flows
Practice Problems to Accompany Slide Set #5
These problems will not be graded
SOLUTION KEY
1. (from RJS) The starting and current tableaus of a given problem are shown below. Find the
values of the unknowns a t

INSY 7420 Linear Programming & Network Flows
Practice Problems to Accompany Slide Set #4
These problems will not be graded
SOLUTION KEY
1. Consider the following LP and corresponding graphical representation:
x2
Max z = 3x1 + 5x2
s.t.
x1
2x2
3x1 + 2x2
x1

INSY 7420/7426 Linear Programming & Network Flows
Practice Problems to Accompany Slide Set #3
These problems will not be graded
SOLUTION KEY
1. (from BJS) Show that the vectors
1
a1 = 0 ,
0
0
a2 = 1 ,
0
1
and a3 = 5
3
0
3
form a basis for R . Supp

INSY 7420 Linear Programming & Network Flows
Practice Problems to Accompany Slide Set #10
These problems will not be graded
SOLUTION KEY
1. [From BJS] Consider the following optimal tableau for a maximization problem, where the
constraints are of the type

INSY 7420 Linear Programming & Network Flows
Practice Problems for Transportation and Assignment
These problems will not be graded
SOLUTION KEY
Problem 1
NOTE:
X
si =
X
dj , so this problem is balanced.
a) Yes, the solution is basic:
There are m + n 1 =

INSY 7420 Linear Programming & Network Flows
Practice Problems to Accompany Slide Set #12
These problems will not be graded
1. [From BJS] Solve the following network flow problem using x13 , x34 , and x42 as part of a
starting basis.
b1 = 3
b3 = 5
c13 = 4

(c) Is the feasible region unbounded?
(d) Draw an isocontour and indicate the direction of improvement.
(e) Does an optimal solution exist? Why (or why not)?
(f) Is the objective function value unbounded?
(g) If an optimal solution exists, clearly mark it

INSY 7420 Linear Programming & Network Flows
Practice Problems to Accompany Slide Set #9
These problems will not be graded
1. Solve the following problem by the dual simplex method:
Min
s.t.
2x1 + 3x2 + 5x3 + 6x4
2x1 + 2x2 + 3x3 + x4
3
x1 + x2 x3 + 3x4 2

INSY 7420, 7426
Linear Programming
Homework 3
Due date:
INSY 7420: Tuesday, April 5th, midnight
INSY 7426: Tuesday, April 12th, at the beginning of the class (3:30pm)
1. Solve equation ex = x2 using Newtons method. When determining the appropriate number

INSY 7420, 7426
Linear Programming
Homework 2
Due date:
INSY 7420: Tuesday, February 23rd, midnight
INSY 7426: Tuesday, March 1st, at the beginning of the class (3:30pm)
1. Suppose a small hospital has 155 bags of blood in stock and a total of 150 patient

INSY 7420 Linear Programming & Network Flows
Practice Problems to Accompany Slide Set #6
These problems will not be graded
SOLUTION KEY
1. Consider the following problem:
Min
s.t.
2x1 x2 + 6x3
2x1 + x2 x3 10
4x1 2x2 + 2x3 16
x1 ,
x2 ,
x3 0
(a) Solve by th

INSY 7420 Linear Programming & Network Flows
Formulation for the Tanker Scheduling Problem (from Slide Set #1)
Parameter Notation
bi Number of ships per day required on route i; i cfw_1, 2, 3, 4. In our problem, b1 = 3,
b2 = 2, b3 = 1, and b4 = 1.
cij N

INSY 7420/7426 Linear Programming & Network Flows
Homework #1
See Canvas for Due Date
Your answers must be typed.
This is a group/team assignment. Teams will be assigned in Canvas.
The document you submit must reflect the work of your team only.
1. A t

INSY 7420 Linear Programming & Network Flows
Practice Problems to Accompany Slide Set #1
1. Bubbas diet requires that all the food he eats come from one of the four basic food groups
(chocolate cake, ice cream, soda, cheesecake). The nutritional content p

INSY 7420/7426 Linear Programming & Network Flows
Homework #3
See Canvas for Due Date
Your answers should be typed or neatly written.
You may form your own teams of up to 4 students.
The document you submit must reflect the work of your team only.
1. U

INSY 7420 Linear Programming & Network Flows
Practice Problems to Accompany Slide Set #8
These problems will not be graded
SOLUTION KEY
1. (from BJS) Give the dual of the following problem:
Max
s.t.
2x1 +
2x1 +
2x1
3x2 + 5x3
x2 + 3x3 + x4
+ x3
2x2 + x3 +

INSY 7420 Linear Programming & Network Flows
Practice Problems to Accompany Slide Set #9
These problems will not be graded
SOLUTION KEY
1. Solve the following problem by the dual simplex method:
Min
s.t.
x5
x6
2x1 + 3x2 + 5x3 + 6x4
2x1 + 2x2 + 3x3 + x4
3

INSY 7420 Linear Programming & Network Flows
Practice Problems to Accompany Slide Set #6
These problems will not be graded
1. Consider the following problem:
Min
s.t.
2x1 x2 + 6x3
2x1 + x2 x3 10
4x1 2x2 + 2x3 16
x1 ,
x2 ,
x3 0
(a) Solve by the Two-Phase M

INSY 7420 Linear Programming & Network Flows
Practice Problems to Accompany Slide Set #8
These problems will not be graded
1. (from BJS) Give the dual of the following problem:
Max
s.t.
2x1 +
2x1 +
2x1
3x2 + 5x3
x2 + 3x3 + x4
+ x3
2x2 + x3 + x4
x1
x2 , x

OA 4202, Homework 4
Nedialko B. Dimitrov
In-class work
1. (AMO)
2. (AMO)
3. (AMO)
4. You are working for a group that has been monitoring a terrorist organization. Your group
has intercepted enough communications and gathered enough intelligence to recons

INSY 7420, 7426
Linear Programming
Homework 3
Due date:
INSY 7420: Tuesday, April 5th, midnight
INSY 7426: Tuesday, April 12th, at the beginning of the class (3:30pm)
1. Solve equation ex = x2 using Newtons method. When determining the appropriate number

INSY 7420
Linear Programming
Exam 1 solutions
Problem 1
Sets and Parameters
i Month index i cfw_1, 2, 3
j Period index j cfw_1, 2, 3
Decision Variables
xij Space amount leased, starting on month i for j periods.
Linear Programming Formulation
min
280(x

INSY 7420
Linear Programming
Homework 1 solutions
Problem 1
Sets and Parameters
i Item index i cfw_1, 2, ., n
ci Street value of item i
wi Weight of item i
vi Volume of item i
M axW Maximum allowed weight (=500)
M axV Maximum allowed volume (=300)

Network Optimization, Homework 2 Solutions
Nedialko B. Dimitrov
1. Run Dijkstras algorithm on the graph in Figure 1 with start node 0. Specifically,
(a) List the order in which nodes are popped off the priority queue.
u).
(b) For each node u, list the se

INSY 7420
Linear Programming
Homework 2 solutions
Problem 1 Part a
Sets and Parameters
i, j Blood type index i cfw_1, 2, 3, 4 (A, B, O, AB)
si Number of bags in stock of the blood type i
di Demand of blood type i
yij A table with 1 and 0 values, which

INSY 7420 Linear Programming & Network Flows
Practice Problems to Accompany Slide Set #5
These problems will not be graded
1. (from RJS) The starting and current tableaus of a given problem are shown below. Find the
values of the unknowns a through n.
St