ESI 4312
Operations Research
Distribution and Network Models: Part
2
Material prepared by Dima Nazzal , IEMS, UCF.
Distribution & Network Models
REMEMBER In the LP Formulation
For each node
FLOW IN = FLOW OUT
Maximal Flow Problem
The maximal flow problem

E81 4312 Sample Exam 2 Sometime
Name (Please Print) PID
1. [20 points] Given the cost table, please use Hungarian method to find the assignment
with least total cost. (You need show which job is assigned to which worker. And give
the minimal total cost.)

Homework II
ESI 4312 Operations Research
Please turn in the homework solutions at the beginning of the class. Late
submission will be penalized. Your homework should be stapled.
1. (25 points) Consider the following LP:
min z = 2x1 5x2 + 6x3
s.t.
3x1 + 7x

Homework III Solutions
ESI 4312 Operations Research
1. (50 points) Consider the following LP:
max z =
3x1 + 2x2
2x1 + x2 100
s.t.
x1 + x2 80
x1 40
x1 , x2 0
In order to bring the problem into standard form, we have to add the slack variables
s1 , s2 and s

Homework III Solutions
ESI 4312 Operations Research
1. (25 points) Consider the following LP:
max z = 3x1 + x2
4x1 + x2 4
s.t.
2x1 + x2 4
x1 + x2 = 3
x1 , x2 0
(a) Solve the problem graphically
(b) Solve the LP using the Big M method.
(c) Identify in each

ESI4312
Quiz 5 Solutions
Name (Please Print)_
PID_
Suppose you are assigned to manage a project, which has 7 activities as follows,
Activity
Description
Predecessors Duration(weeks)
A
Finish the foundation
5
B
Build the walls and ceilings
A
8
C
Build the

Homework I Solutions
ESI 4312 Operations Research I
1. (20 points)
Decision Variables:
1 : number of hours production unit 1 is used
(1)
2 : number of hours production unit 2 is used
(2)
Objective function:
The sum of the cost of the two running processes

Fall 2016
Sep 1st
Quiz 1 Solution
Name (Please Print)_
UCFID_
1. Farmer Joe needs to plant both corn and rice in the next summer. Market price of corn is
$.6/lb and $.8/lb for rice. Every acre can yield 1000lb corn or 800lb rice in one summer.
Joe needs a

ESI4312
Quiz 3 Solutions
Name (Please Print)_
2016
NID_
1. Given a linear program as follows,
Max = $ + &
s.t. 2$ + & = 3,
$ + 2& 2,
$ , & 0,
a) After transform the above LP into standard/equation form, find all the basic solutions
and their corresponding

ESI4312
Quiz 4 Solutions
Name (Please Print)_
PID_
1. A network is given as follows, where the numbers on arcs are the unit costs. Find the
shortest paths from node 0 to all other nodes by Dijkstras algorithm. (No point will be
given if steps of Dijkstras

ESI4312
Sep 22nd, 2016
Quiz 2
Name (Please Print)_
UCF NID_
1. Given a linear program as follows,
Max = $ + &
s.t. 2$ + & = 3,
$ + 2& 2,
$ , & 0,
After transform the above LP into standard/equation form, find all the basic solutions
and their correspondin

ESI 5306
Operations Research
LP Applications
University of Central Florida
Orlando, FL
Material prepared by Vernet Lasrado, UCF.
Topics Covered
Diet Problem
Workforce
Marketing Applications:
Assignment
Blending Problem
Media Selection
Marketing Research
F

ESI 5306
Operations Research
Simplex Method
University of Central Florida
Orlando, FL
Material prepared by Vernet Lasrado & Dima Nazzal, IEMS, UCF.
Overview of the Simplex Method
Steps Leading to the Simplex Method
Formulate
Problem
as LP
Put In
Standard

ESI 5306
Operations Research
Duality
University of Central Florida
Orlando, FL
Material prepared by Vernet Lasrado, Dima Nazzal , IEMS, UCF.
Canonical Form
A maximization linear program is said to
be in canonical form if all constraints are
less than or e

Homework II
ESI 6418 Linear Programming & Extensions
1. Consider the following LP:
min z = 2x1 5x2 + 6x3
s.t.
3x1 + 7x2 + x3 1
5x1 + 3x2 x3 10
2x1 + 5x2 = 12
x1 , x2 0, x3 unrestricted
(a) Bring the LP to standard form.
(b) Suppose the objective function