Assignment 6
1 Production model:
Two products are to be produced, Product A and product B. Their unit prices on the
market are 60 and 80 respectively. Each product takes one unit of wood and the total
amount of wood available is 80. But each product B req
Assignment 6 solutions
1 Production model:
Two products are to be produced, Product A and product B. Their unit prices on the
market are 60 and 80 respectively. Each product takes one unit of wood and the total
amount of wood available is 80. But each pro
CEE 6930 Exam November 21
Name:_
Please answer each question in the space provided.
1. Given the demand function
10
3
Unit Price $
:
1/6
a) (3) What does any demand function signify?
1
0
X
The amount of X that will be sold at a given price.
b) (3) What is
Assignment 5 Equilibrium
1. Forest Management:
In a particular town watershed there exists two competing tree species: hardwoods
and softwoods. The watershed is managed primarily to produce clean water, but it also
serves as wildlife habitat and source of
Assignment 2
Dynamic Programming due 14 Sept.
1. Consider again the resource allocation problem where we want to maximize (6x x2)
+ (7y 1.5y2) + (8z 0.5z2) subject to: x + y + z R, where R is the amount of resources
available. Show how you would use dynam
Assignment 4 Problems involving model building and solving using calculus and
LINGO
1. A North Carolina farmer is raising pigs. Today her average pig weighs 200 pounds
and gains 5 pounds per day. The current price per pound is $0.65 however the price
seem
Assignment 5 Difference Equations solutions
1.
Forest Management:
In a particular town watershed there exists two competing tree species: hardwoods
and softwoods. The watershed is managed primarily to produce clean water, but it also
serves as wildlife ha
Assignment 7a
1. The classic transportation problem.
You as an employee of the Department of Homeland Security (DHS) are in charge of
maintaining the readiness of emergency supplies at various distribution sites within a
region that may be subjected to na
Assignment 8 Simulation, Probabilities and Statistics
Read Ch 6 on simulation.
1. Warm up
Consider the symmetric triangular probability density function that ranges from 0 to 10
whose mean and most likely value is 5.
fX(x)
0
5
10
x
Define and sketch the c
Assignment 5 Problems involving calculus 1. A North Carolina farmer is raising pigs. Each day her average pig adds 5 pounds per day. Today the average pig weighs 200 pounds. The current price per pound is $0.65 however the price seems to be decreasing by
Assignment 4 Problems involving model building and solving using calculus and
LINGO
1. A North Carolina farmer is raising pigs. Today her average pig weighs 200 pounds
and gains 5 pounds per day. The current price per pound is $0.65 however the price
seem
CEE 6930; PADM 5320 Public Systems Modeling Spring 2016
HEB 101 MVR
TR 8:40-9:55
4 Credits
Course Objectives: The course serves as an introduction to the art of model building and use,
especially related to the analysis of public sector planning and manag
Exercise 6 due Oct.8th
Yangtian Li
yl2492
1. Answer: The U.S. population will reach 400,000,000 at Saturday,
April 28th, 2040, which is 10118.19 days after August 14th, 2012.
Let x denote the number of days after 08/14/2012.
Command:
birth=x/7;
death=-x/1
Time value of money
Congratulations! You have won a cash prize! You have two payment options:
A. Receive $10,000 now
OR
B. Receive $10,000 in three years.
Okay, the above offer is hypothetical, but play along with me here . Which option would you
choose?
Notes for class on 26 August:
Discuss syllabus
Homework exercises: Assume you are responding to your employer (i.e., readable and
neat). State (copy) problem before giving your answer.
Modeling example: Generating retirement income using a Roth IRA.
Roth
Exercise due September 30.
a. Production model:
Solution:
Model:
Max total profit=60A+80B
Subject to: Material constraint: A+B<=80;
Labor constraint: A+2B<=280;
Non-negativity constraint: A>=0; B>=0;
LINGO:
Hence, the production of A is 0 and the producti
Exercise
Yining Wang
ID: 4051508 NetID: yw738
How much money will you need when you retire and how are you
going to get it?
Roth IRA (Individual Retirement Account): Tax-free investing.
Can invest a maximum of $5000/year of earned income.
Two risks: Infla
PADM 5320
Exercises due September 9.
1. As a member of the Town of Ithaca Planning Board, suppose you want to allocate public
funds (money) to three public sector organizations or activities. Each organization provides a
unique service that the public is
Exercises due September 16
1. Consider the same allocation problem as in last weeks exercise: The benefits derived from
allocating X to the first organization are 15X-3X2. For the second organization they are 9Y Y2,
and for organization 3 they are 11Z Z2
Systems Modeling
Introduction
What is a system and why model systems?
Examples of public systems might include:
water supply and wastewater systems (Town of Ithaca)
health systems (Medicare, Medicaid, Tricare)
emergency alert systems (in Airports, bus sta
Mathematical Symbols
This course involves some mathematics, and like many disciplines there are some symbols that
are used to represent operations, such as addition, multiplication, differentiation, integration, etc.
For those whose exposure to math may h
Mathematical Modeling
Introduction
A mathematical model is a mathematical representation of a system, possibly together with
expressions defining measures of system performance, i.e., the impacts resulting from the design
and operation of the system. The
Notes for 23 Sept.
-Unit
Price p
Po
Unit price = Po - bq
b
1
0
q* Quantity q
0
Suppose you want to find the area under the demand function up to some value of q.
Willingness to pay = area under demand curve. (Po bq for no negative WTP.)
Using geometry:
Wi
Differences between hill climbing, flow diagram and dynamic programming network
Yangtian Li
All of the three are mathematical optimization methods, while their respective features are as
follows.
a. Hill climbing (see Page 3, Chapter 5)
Using the approach
Mathematical Modeling Software
Introduction
There are many systems models that do not lend themselves to solution by the hill climbing,
calculus-based, or dynamic programming methods presented in the previous chapters. In such
cases we can take advantage
Lagrange Multipliers
Joseph-Louis Lagrange is usually considered to be a French mathematician, but the Italian
Encyclopedia refers to him as an Italian mathematician. 1736 - 1813
In Paris a street on the left bank is named after him. Rue Lagrange
Lagrange
Some example models and their solutions
Saving for retirement
Generating retirement income using a Roth IRA.
Roth IRA (Individual Retirement Account): Tax free investing. You can invest a maximum of
$5500/year of earned income. You decide how to invest an
Calculus/Differentiation
Introduction
We can use some procedures included in what is termed calculus to find the slope of any
function. Why do we care about slopes of functions? Because many decisions are
based on the slopes of functions (i.e., their marg