To promote onaeampus sarery, the U oft security department is in the process or installing
emergency telephones at selected locations The depamnent wants to install the minimum
number of telephones provtded that each of the campus main streets is served b

6.1-5(a.)Construct dual problem for primal problem.(b)Solve the dual graphically and use this solution
To identify the shadow prices for the resources in the primal problem.
6.1-14(a)The sum of the number of functional constraints and the number of variab

56:171 Operations Research
Exam 3
8:00~9:30 pm, December 10, 2012
NOTES:
1. Two-page formula sheet is allowed.
2. Write your answer on this exam paper. DO NOT use your own paper. If you need more
space, write on the backside of this exam paper.
3. The tes

IE:3700 Operations Research
Instructor: Yong Chen
MWF 12:30 - 1:20pm
Fall 2016
1
My Background
B. E. in computer science, Tsinghua
University, China, 1998
Ph. D., 2003, Industrial and Operations
Engineering, University of Michigan
Now Professor in Dept.

Assumption of LPs
When we write a problem as a linear
program, we are making a few assumptions
about the underlying process
Proportionality: The contribution of a decision
variable to the objective function or any one of
the constraints is proportional to

Theory of the Simplex
Method
For any LP with feasible solutions and a bounded
feasible region:
If there is exactly one optimal solution, then it
must be a corner-point feasible (CPF) solution
If there are multiple optimal solutions, then at
least two must

No Feasible Solutions
Min Z = 2x1 + 3x2
s.t.
x1 + x2 4
x1 + 3x2 36
x1 + x2 = 10
x 1 , x2 0
An LP is infeasible if an artificial variable
is greater than zero in a final solution
x1
x2
s1
e1
a1
a2
RHS
-Z
2M-1
0
0
M
0
4M-3
-30-6M
s1
1/4
0
1
0
0
-1/4
3/2
a1

Introduction to Excel Solver
86
Loading Solver
The Solver Add-in is a Microsoft Office Excel add-in
program that is available when you install Microsoft
Office or Excel. To use it in Excel, however, you need to
load it first.
Click the Microsoft Office Bu

The Smalltown Fire Department currently has 4 old ladder companies and 4 alarm boxes. The For a minimization integer programming problem, the optimal Z value of its LP max * X5 *1; +41: 5.1.
Consider the following nonlinear programming problem:
zlxzxfxg 2