Blending of Input Materials
In a blending problem, there are:
1) Two or more input raw material commodities;
2) One or more qualities associated with each input commodity;
3) One or more output products to be produced by blending the
Sample Linear Programming Problem
A furniture manufacturer makes two types of furniture chairs and sofas. The
production of the sofas and chairs requires three operations carpentry, finishing, and
upholstery. Manufacturing a chair requires 3 hours of carp
A LINGO model that can be used to maximize the profit in this situation is:
Math 3171 Assignment #6-Computer Assignment
This assignment is intended to determine if you are able to use LINDO 6.1 efficiently to solve an LP
problem. You must hand in this assignment to show proficiency in LINDO before I will report a
grade for you in
Section 4: The Simplex Method (Ch.4 of text) and includes a further
review of linear algebra
A. Aim and Methodology
1. proceed from one corner point (extreme point) to another in a
manner that the objective function which we want to minimize is
Section 5: Sensitivity Analysis and the Simplex Tableau
Question: What can we get out of the Simples Tableau:
1. OPTIMAL BASIC FEASIBLE SOLUTIONS IF THEY EXIST
2. VALUE OF OBJECTIVE FUNCTION AT O.B.F.S.
3. STATUS OF RESOUCES
4. MARGINAL WORTH (S
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MATH 3171 3.00 A
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The Model Formulation
Count what is countable, measure what is measurable, and
what is not measurable, make measurable.
4.1 The Overall Process
In using any kind of analytical or modeling approach for attacking a probl
3.1 Economic Analysis of Solution Reports
A substantial amount of interesting economic information can be gleaned from the solution report of a
model. In addition, optional reports, such as range analysis, can provide further informa
Product Mix Problems
Product mix problems are conceptually the easiest constrained optimization problems to comprehend.
The Astro/Cosmo problem considered earlier is an example. Although product mix problems are
seldom encountered in th
What Is Optimization?
Optimization, or constrained optimization, or mathematical programming, is a mathematical procedure
for determining optimal allocation of scarce resources. Optimization, and its most popular special
form, Linear Pr
One of the most important uses of optimization is in multi-period planning. Most of the problems we
have considered thus far have been essentially one-period problems. The formulations acted as if
February 27, 2008
Some Simplex Method Examples
Example 1: (from class) Maximize: P = 3x + 4y subject to:
2x + y 5
x 0, y 0
Our rst step is to classify the problem. Clearly, we are going to maximize our objective function, all are variables ar
Question 1 [5 rnarks]
e d Y
Factories A, B and C produce up to 100,200, and 50 units.
Units may sent to destinations D, E, or F. Destinations D, E and F must rec
Solutions to selected Homework Problems
from Sections 3.8 and 3.9 of the textbook.
# 10. Let Mi = tons of coal shipped from Mine i and
Xij = tons of coal shipped from Mine i to Customer j.
Here is the appropriate formulation of the problem in
Solutions to selected Homework Problems
from Sections 3.2, 3.8, 3.10 and 3.11 of the textbook.
4a) We want to make x1 larger and x2 smaller so we move down and to the right.
4b) We want to make x1 smaller and x2 larger so we move up and t
Solutions to Homework Problems
from Sections 4.4 of the textbook.
From Figure 2 of Chapter 3 we see that the extreme points of the feasible region and
corresponding Basic Feasible Solutions are:
H = (0, 0) - s1 = 100, s2 = 80, s3 = 40, x1 = x2 = x3 =
1. Since we wish to move from one basic feasible solution to an
adjacent bfs, we do so by moving from one extreme point to an
adjacent extreme point. This corresponds to interchanging one basic
variable x with one non-basic variable x . x is c