Math 220, Loeb Lecture 1, August 23, 2006
1
1. Homework and Notes on the Web
The code books for the homework will come into the bookstores today and tomorrow.
Remember, your homework is worked at the address
http:/phga.pearsoncmg.com/phga/classes/Math220D
Math 220, Loeb Lecture 22, October 13, 2006
1
1. Come to Class
Starting next time, we will cover material in a way that is not in the book. Come to
class.
2. A Tutoring Room is Open
7 p.m, Monday, Tuesday, Wednesday, Thursday, Room 140 Lincoln Hall.
9
3.
Math 220, Loeb Lecture 23, October 16, 2006
1
1. Come to Class
Starting next time, we will cover material in a way that is not in the book. Come to
class.
2. A Tutoring Room is Open
7 p.m, Monday, Tuesday, Wednesday, Thursday, Room 140 Lincoln Hall.
9
3.
Math 220, Loeb Lecture 21, October 11, 2006
1
1. Problems with entering homework
If you believe that you have entered a correct answer for the homework that the
website will not accept, be sure you have carefully read the problem and the format
needed. If
Classical Optimization
Theory
Nur Aini Masruroh
Scope
Continuity vs discontinuity
Unimodality vs multimodality
Local optimum vs global optimum
Convex (concave function)
Hessian matrix
Necessary and sufficient conditions for convexity
Constrained problem
C
+
OPTIMIZATION
Nur Aini Masruroh
+
An Opening Story
Tortoise vs Hare: Who is faster?
Once
upon a time a tortoise and a hare had an
argument about who was faster.
Settle
the argument with a race.
Agreed
on a route and started off the race.
The
hare was
Queuing Theory
Nur Aini Masruroh
Outlines
Introduction
Birth-death process
Single server model
Multi server model
Introduction
Involves the mathematical study of queues or waiting
line.
The formulation of queues occur whenever the demand
for a service e
REVISED SIMPLEX
METHOD
NUR AINI MASRUROH
LINEAR PROGRAMMING
What is linear programming?
Concerned with the determination of the best allocation of scarce
resource
Special condition linearity
Linear expression
2x1 + 3x2 x3 + 5
Nonlinear expression
x
Scope
0 One dimensional unconstrained optimization
0 Direct method/value function based method: bracketing
method
0 Newton method
0 Secant method
0 Multidimensional unconstrained optimization
0 Gradient method
0 Newton method
Two different methods for sea
Operations Research 1
Sinta R Sulistyo, ST, MSIE
sinta.sulistyo@ugm.ac.id
Last Lecture
LP Model
Graphical Solution
Todays Outline
Simplex method (for maximization)
Simplex for minimization
Big M Method
Duality*
Sensitivity Analysis*
Simplex Algori
RISET OPERASI
Sinta R Sulistyo
sinta.sulistyo@ugm.ac.id
Last Lecture
LP Modeling
Graphical Solution
Simplex for Maximize Problem
Todays Lecture
Simplex for Minimization Problem
Big M Method
Sensitivity Analysis
Duality
Announcement
Some adjustment
Riset Operasi
Sinta R Sulistyo
sinta.sulistyo@ugm.ac.id
Last Lecture
LP Modeling
Graphical Solution
Simplex for Maximize (and Minimize) Problem
Big M Method
Sensitivity Analysis
Duality
Todays Lecture
Transportation
Transportation Problem
Transport
Homework 1
Due date: 31 August 2016
Problem 1
There are three factories on the Momiss River (1, 2, and 3). Each emits two types of pollutants (1 and 2)
into the river. If the waste from each factory is processed, the pollution in the river can be reduced.
Math 220, Loeb Lecture 20, October 9, 2006
1
1. Dropping or Dropping Down the Course
For students who are having di culty in this course:
Students may drop down to Math 016 (no credit toward graduation but hours
count for full-time student status) until T
Math 220, Loeb Lecture 18, October 4, 2006
1
1. Dropping or Dropping Down the Course
For students who are having di culty in this course:
Students may drop down to Math 016 (no credit toward graduation but hours
count for full-time student status) until T
Math 220, Loeb Lecture 17, October 2, 2006
1
1. Dropping or Dropping Down the Course
For students who are having di culty in this course:
Students may drop down to Math 016 (no credit toward graduation but hours
count for full-time student status) until T
Math 220, Loeb Lecture 4, August 30, 2006
1
1. Homework that was due August 29
The homework system was down the evening of August 28. Almost everybody did
the rst homework before that, and got full credit. To be fair, I will give everybody
full credit for
1
Math 220, Loeb Lecture 6, September 6, 2006
1. A Tutoring Room is Open
7 p.m, Monday, Tuesday, Wednesday, Thursday, Room 140 Lincoln Hall.
9
2.
Homework 4 due Thursday, September 7 at 9 a.m.
Section 2.1: #10, 16.
Section 2.2: #24, 38. Give exact answer.
Math 220, Loeb Lecture 5, September 1, 2006
1.
1
Homework due Thursday, August 31 at 9 a.m.
Section 1.3: #4, 8, 10, 12, 14, and 16.
Section 1.4: #14, 16, 22, and 24.
This second homework with graphs is now online as HW2NewAug31. You will go
over this home
Math 220, Loeb Lecture 16, September 29, 2006
1
1. Dropping or Dropping Down the Course
For students who are having di culty in this course:
Students may drop down to Math 016 (no credit toward graduation but hours
count for full-time student status) unti
Kuis Riset Operasi
Take Home Exam (DUE: 22 September 2016. Kumpulkan ke meja mbak Yanti maks pukul 15.00)
1.
Tani Maju memproduksi dua tipe makanan ternak, keduanya terbuat dari dua macam bahan baku yaitu
protein A dan protein B. Makanan ternak tipe 1 har