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
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
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
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 amou
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 wate
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
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
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
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 poun
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 li
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 distrib
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
Exercises due September 20, 2017
1. Pigs:
It seems Cornell runs an organic farm that produces pigs. They raise, butcher, and sell the meat
to Cornell Dining, thereby contributing to Cornells 3rd best
Probability and Statistics
Introduction
When the outcome of an event or system is not predictable, we often call it random. If we
observe many outcomes we can define the probability distribution of ou
PADM 5320: Exercises due September 6, 2017
1. Identify a specific multi-component system and show the links among the interdependent
components. This is called a conceptual model.
The public transport
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 pl
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,
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, i
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 rela
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 o
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 exampl
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;
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 m
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
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
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 org
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
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
V Fuzzy Optimization
1
2
3
4
5
6
7
FUZZINESS, AN INTRODUCTION.1
OPTIMIZATION IN FUZZY ENVIRONMENTS.3
FUZZY SETS IN WATER ALLOCATION.5
FUZZY SETS AND RESERVOIR STORAGE AND RELEASE TARGETS.7
FUZZY SETS
Equilibrium Difference Equations
Introduction
When a system is in equilibrium there is no change in the values of its output over time or
those values become periodic and predictable, or if random, th
!max = A + 2*B; ! max = 2*A + B;
A + B < 4; A + 2*b < 8;
max = A + EBR;
Variable
A
B
B
$
2
Row
1
2
3
1
4
0
0
4
8
Row
1
2
3
A
Reduced Cost
0.000000
0.000000
Slack or Surplus
8.000000
0.000000
0.000000
Discrete Dynamic Programming
Dynamic programming is an approach that transforms a multi variable optimization problem into
a sequence of single variable optimization problems. Discrete dynamic program