Example 1, Section 4.16
The Leon Burnit Ad Agency is trying to determine a TV schedule for Priceler Auto.
Ad
HIM LIP HIW
Cost
Football
7
10
5
100, 000
3
5
4
60, 000
Soap Opera
Goals
40
60
35 600, 000
This means, for example, that the ad agency wants to re
6.5: Construction of the Dual
Here is the problem well work on:
minx 8x1 + 5x2 + 4x3
s.t. 4x1 + 2x2 + 8x3
7x1 + 5x2 + 6x3
8x1 + 5x2 + 4x3
3x1 + 7x2 + 9x3
= 12
9
10
7
x1 0, x2 URS, x3 0
First well take care of the sign restrictions so that all of our vari
Final Exam, Operations Research (Fall 13)
This is a take home exam. You may use your text, any class notes and anything on our class
website to help, and you may use LINDO, Maple and/or Matlab. You should not look for
solutions on the internet, or get hel
Solutions to Review Questions, Exam 1
1. If x = [1, 1, 0, 2]T and y = [2, 1, 0, 4]T , then compute the distance from x to y using
the (a) 1-norm, and (b) the innity norm.
SOLUTION:
xy
1
= |1 2| + | 1 + 1| + |0 0| + |2 4| = 1 + 0 + 0 + 2 = 3
xy
= max cfw_1
Review Solutions, Exam 2, Operations Research
1. Prove the weak duality theorem: For any x feasible for the primal and y feasible for the
dual, then.
HINT: Put the primal so that Ax b and the dual so that AT y c
SOLUTION: With the primal and dual in norma
Review Material, Exam 2, Ops Research
1. Prove the weak duality theorem: For any x feasible for the primal and y feasible for the
dual, then.
HINT: Put the primal so that Ax b and the dual so that AT y c
2. Show that the solution to the dual is y = (cT B
Review Material, Exam 1, Ops Research
The exam will cover material from Chapter 3 (we skipped 3.6, 3.7), up through section 4.8.
Background Material: Linear Algebra
Though these may not be asked explicitly, you should be able to do the following (and may
HW Set 3 Solutions
3.10, 7 Let st be the pairs of shoes made during quarter t.
Let it be inventory of pairs of shoes at the end of each quarter.
Let xt be the number workers getting quarter t o during each year. So, for example,
x1 would be working all qu
Homework Solutions to Section 3.1-2
These are the solutions to the problems not turned in: 3.1- 1, 5 and 3.2-1, 2, 4
3.1 Solutions
1. In this case, x1 , x2 are given to you- Normally, you would want to dene those terms rst.
Let x1 , x2 be the number of ac
Operations Research
Prof. D.R. Hundley
Whitman College
Fall 2013
DRHundley (WHI)
Math 339
10/16/2013
1 / 18
Introduction
We started this last time:
Were buying advertising time for HIW and HIM.
Let x1 , x2 be the number of ads purchased during a comedy sh
Matrix Notation and Simplex (6.2)
Prof. D.R. Hundley
Whitman College
Fall 2013
DRHundley (WHI)
Math 339
10/16/2013
1 / 14
Introduction
Consider the LP in standard form,
max z = cT x
st Ax = b
x0
where A is m n with rank m. We will re-partition these matri
Scientic Applications of LP
These notes will show how to interpret curve tting problems as linear programs. In order
to start, we need to dene dierent ways of measuring the error between an unknown set of
points in the plane:
cfw_(x1 , y1 ), (x2 , y2 ), (
Homework Solutions to Section 3.9
1. Dene variables rst. In this case, we need to know the hours to run each process per week,
and the barrels of stu being bought/sold. In this case, we might dene:
x1
x2
x3
g2
o1
o2
Hours of Process 1 run per week
Hours o
Example 2, Section 4.16 (Goal Programming)
The Dewright company is considering three new products to replace current models. Primary consideration should be given to three factors:
Long-run prot of at least 125 million dollars.
Maintain current employme
Homework Solutions to Section 3.3-3.5
These are the solutions to the problems not turned in.
3.3 Solutions
1. Does this LP have a unique solution? If not, why
a description will suce).
max z = x1 +
s.t.
x1 +
x1
x1 ,
not (the text asks us to use Cases 1-4