Mathematical Optimization Problem
The mathematical optimization problem involves
choosing values of certain variables to optimize a
function subject to constraints.
The variables are called instruments.
The function to be optimized is the objective fun
ECONOMIC DECISIONS
AND MATHEMATICAL
OPTIMIZATION PROBLEMS
SCOPE OF MANAGERIAL ECONOMICS
Douglas : Managerial economics is . the
application of economic principles and
methodologies to the decision-making process
within the firm or organization.
Hirschey
Mathematical Optimization Problem
The mathematical optimization problem involves
choosing values of certain variables to optimize a
function subject to constraints.
The variables are called instruments.
The function to be optimized is the objective fun
INTEGER LINEAR PROGRAMMING
Variables may assume continuous or integer
values.
Addition of integrality condition
INT(Xi) = largest integer that is less than Xi
VOF (x*)ILP VOF (x*)LP if max problem
VOF (x*)ILP VOF (x*)LP if min problem
Branch-and-bou
PRODUCTION
AND COST ANALYSIS
PRODUCTION FUNCTION
Q f ( x, y )
The maximum output that can be produced
for a given amount of input.
Discrete vs. continuous
Returns to scale vs. Returns to a factor
Law of diminishing returns
PRODUCTION FUNCTION
Isoquan
OUTPUT ELASTICITY
% change in output
Q
% change in all inputs
Q / Q
I / I
Q I
I Q
Q > 1 increasing RTS
Q = 1 constant RTS
Q < 1 decreasing RTS
COST ELASTICITY
% change in cost
C
% change in output
C / C
Q / Q
C Q
Q C
C < 1 increasing RTS
C = 1 constant
Lecture HO model
Factor Proportions Trade Model
Outline
Factor intensity
Factor endowment
Neoclassical theory of trade
Assumptions behind the HO Model
Two goods, X and Y; two countries, H and F, and two factors, L
and K.
Both countries have the same produ
ECONOMIC DECISIONS
AND MATHEMATICAL
OPTIMIZATION PROBLEMS
SCOPE OF MANAGERIAL ECONOMICS
Douglas : Managerial economics is . the
application of economic principles and
methodologies to the decision-making process
within the firm or organization.
Salvator
EMPLOYEE SCHEDULING
(Ragsdale, p. 277) Snookers Restaurant is open from 8:00 am to
10:00 pm daily. Besides the hours that they are open for
business, workers are needed an hour before opening and an hour
after closing for setup and cleanup activities. The
Example 1
Solve the following linear programming problem by
solving the dual problem:
min G = 6y1 + 20y2 + 3y3 + 20y4
subject to
3y1 + 6y2 - y3 + 2y4 4
-4y1 + 2y2 + y3 + 5y4 2
yi 0 i = 1, ., 4
Example 2:
Given the problem:
max c0 = x1 + 2x2
subject to
x1
Use of Artificial Variables
When the computational form of the LPP is not canonical
with respect to some basic sequence, artificial variables are
used. This happens in 2 cases:
a) the original problem is a minimization problem; and
b) one of the constrain
MINIMAL SPANNING TREE PROBLEM
80
B
60
A
55
C
D
70
75
95
90
60
E
H
85
60
G
90
50
70
75
65
45
120
F
80
I
J
ALGORITHM
MINIMAL SPANNING TREE PROBLEM
(1)Pick any node as the initial connected
node.
(2)Identify all arcs joining a connected node
with an unconnec
Thm. If x is primal feasible and y is dual feasible then
VOF(x) VOF (y), i.e., the minimand can never fall below the
maximand.
Thm. If x* is primal feasible and y* is dual feasible, and
VOF (x*) = VOF(y*), then x* and y* are optimal solutions.
Thm. If the
GOAL PROGRAMMING
MULTIPLE OBJECTIVE LINEAR PROGRAMMING
Enabling Business, Empowering Consumers
2
GOAL PROGRAMMING
1. James Furniture produces tables and chairs using
wood and labor. He has 300 units of wood and 110
hours of labor available for production
Name: _ Date: _
1. The Columbus Zoo conducts a study to determine whether a household's income can be
used to predict the amount of money the household will give to the zoo's annual fund
drive. The response variable in this study is
A) the Columbus Zoo.
B
Name: _ Date: _
Use the following to answer question 1:
For a physics course containing 10 students, the maximum point total for the quarter was 200. The
point totals for the 10 students are given in the stemplot below.
1. This stemplot is most similar to
Density Curves, mean and
median
AP Statistics
A density curve is a curve that
Is always on or
above the horizontal
axis and,
Has an area of 1
underneath it
Describes the
overall pattern of a
distribution
Mean vs Median and density
curves
In a symmetri
_
1. The pie chart describes the distribution of state tree types for the 50 states in the United States.
The category Other include all trees that are the state tree for two or fewer states. Which of the
following conclusions can we draw from this chart?
17-1 Electrostatic Potential Energy and
Potential Difference
Potential energy can be
defined
PE W
Change in electric potential
energy is negative of work
done by electric force:
Electric potential is defined as potential
energy per unit charge:
Unit of el
23
1. A unique aspect of amino acid metabolism involves removal of the amino group.
Know aspects of this as discussed in class including the role of glutamate,
transaminations, glutamate dehydrogenase, urea cycle.
Where do these occur and how is the proce
Intro to Microeconomics
Exam I
Economics more like a social sciences
Study of human behavior in market situations
Almost all waking hours are spent in market situation
In economics, we make assumptions
We act rationally in the market
o Interested in se
H I mar | IFEE
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