Optimization, Homework 2
Problem 1
First, I instantiate slack variables and define the constraints as equalities:
cfw_
x 1 + x 2+3 x 3 +u=6
5 x 1 +3 x2 +6 x 3 +v =15
I now re-write the objective function:
5 x 13 x 2x 3+ z=0
I now create the simplex table:

Optimization, Homework 1, 9/28/16
Problem 1
First, let me clarify what I believe is an ambiguity in the problem: I will interpret it costs $40 to purchase
each 1,000 barrels of oil to mean that each individual barrel con sts $.04; you stated online that w

Optimization, Homework 1, 9/28/16
Problem 1
First, let me clarify what I believe is an ambiguity in the problem: I will interpret it costs $40 to purchase
each 1,000 barrels of oil to mean that each individual barrel con sts $.04; you stated online that w

IEOR 4004
Simplex Method: duality
1
Pricing interpretation
Consider a manufacturing problem with two resources, blocks of wood and cans of paint, and two products,
toy soldiers and toy trains.
Manufacturer
Max 3x1 + 2x2
x1 + x2 80 [wood]
2x1 + x2 100 [pai

IEOR 4004
Formal Simplex Method
Here we outline key steps in the Simplex Method applied to an LP in standard form:
max z = cT x
Subject to:
Ax = b
x 0.
Here A is an m n matrix.
Step I. Find an initial basic feasible solution. This is not a trivial step. A

1
IEOR 4004
Lecture 1 - Introduction to Optimization
Example 1. Cash flows
We have $100 to invest. There are three investment vehicles.
a. for every $1 invested now, we get 0.1 one year from now, and $1.3 three years from now.
b. for every $1 invested now

IEOR E4004 Optimization Models and Methods
HW1: Due Lecture 6 (September 28)
Professor Daniel Bienstock
September 20, 2016
Notes
Each HW must be submitted at the beginning of the class it is due. Late submissions
will not be accepted.
You are allowed to

0.1. FROM LAST LECTURE
1
IEOR 4004
Lecture 2 - Basic Linear Programming Formulations
0.1
From last lecture
Example: maximum throughput supply chain. A food company owns three warehouses with limited space for
storage of a perishable good (fish, say). Ware

IEOR 4004
Lecture 3 - Intro to Linear Programming Algorithms
1
Motivation
We assume an LP in standard form:
(LP):
Subject to
max wT x
(1a)
Ax = b
x 0.
(1b)
(1c)
Here we are assuming that A has m rows and n columns, and so x Rn and b Rm . The
algorithmic i