SYS5110 Fall 2016 Java Assignment
Due: Oct 31, 23:59
Instructions
Submit the assignment via Blackboard Learn and ensure that all Java files are identified with your
name and student number (in comments). In addition to developing a number of Java class fi
SYS5110 Foundations on Modelling and Simulation
Java Exercises, Liang Chapters 9 and 10
Fall 2015
Use an array to pass all values to the LinearEquation constructor and an array to store the
parameter values. Define within the LinearEquation class a set of
SIMPLEX
METHOD
AND
LINEAR
PROGRAMMING
Zhijie Cui, Ci Lin, Xiaojin
Shan
2
Introduction For Simplex Method
WhatNeed
Why
is Simplex
Simplex
Method?
Method?
In practice,
To
solve thereal-world
Linear Programming
problems commonly are complex that
Problem,
wit
Zhijie Cui
Parking Lot Design Documentation
By Zhijie Cui 8420700
Package<parking>
Class Summary
Class
Car
ParkingLot
ParkEvent
ParkEventList
Description
The Car class use to create objects
representing cars.
Contains ParkingLot class used to create
a Par
Simplex Method and Linear Programming
1. What is Simplex Method?
Linear Programming Problem may have infinite feasible solutions, while the finite
vertexes correspond to the basic feasible solutions. In Simplex Method, we start from
one of the basic feasi
SYS5110 Foundations on Modelling and Simulation
Java Exercises, Liang Chapters 7 and 8
Fall 2015
[]
Ensure that the arrays are not modified when the method equals is executed.
Hint: Arrays is a standard Java class that can provide useful methods to manipu
Simplex Method and Linear Programming
1. What is Simplex Method?
Linear Programming Problem may have infinite feasible solutions, while
the finite vertexes correspond to the basic feasible solutions. In
Simplex Method, we start from one of the basic feasi
SYS5160
Systems Integration
Dr. Ali Abbas
Systems Integration
School of Information Technology and Engineering
University of Ottawa
1
Systems Integration
System integration (SI) is essential to the development of large,
complex engineered systems.
It co
SYS5160
Systems Integration
Ali Abbas
aabbas@uottawa.ca
School of Information Technology and Engineering
University of Ottawa
1
What is Integration
Integration (from the Latin integer, meaning whole or entire)
generally means combining parts so that they
SYS5160
Systems Integration
Systems Engineering and
Integration
School of Information Technology and Engineering
University of Ottawa
1
Systems Engineering and Integration
Process
Is a logical sequence of activities and decisions that
transforms an opera
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for?" :16.
Induction Step: We need to show that
771 2'
13(5) >15) =ZBMOJ) for r: k+ 1.
i=0
We have
00 Ak'H miceA1
P(Sk+1 > t) = / de.
t .
Use an integration by parts with 'U. : AkH
Assignment 3
W
a. Result:
There are 6 nodes, and 8 arcs in this networkl
Nodes with Nonzero Demands or Supplies.
Node # Supply(or demand if positive)
1 60
4 10'
5 30.
6 20.
From To
Arc# Node# Node# Cost FixedCost Capacity Multiplier Solution
1 1 2 0 100.
1. [10 points] Consider a small store that receives 4 copies of a local
newspaper daily. Suppose that the customers that would like to purchase
the newspaper can be modeled as a Poisson process with a rate of 3
customers per day. We assume that copies of
7. (3 points) Suppose we have three projects: F, M, D. The value 0 means not selecting
the project, and 1 means selecting. Write down logic conditions to each of the following:
(i) At least one project is undertaken;
(ii) If you make the project M, then y
4. (2 points) Consider the following system:
Maximize 7x1+ 9x2
Subject to xl +x2 s 6
5x1 + 9x2 S 44
xnxz 2 0 integer.
To nd Gomory cuts, we change the two inequalities as:
x1 + x2 + sl = 6
5x1+9x2 +52 =44
51,32 2 0 integer.
By eliminating x2, we obtain
4x
Family Name First Name
Student #
SYS 5130 Midterm-October 14, 19:00-20:30
Closed Book
(In total you have 8 questions, 20 marks in total.)
1. (2 points) True/False:
(a) Any optimization problem has at least one variable. T
(b) Optimization problem may
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Suggested Exercises
Continuous Models
. The time waiting in the emergency room of a hospital before one is
called to see a doctor often seems to be exponentially distributed with
mean equal to 60 minutes. Let X be the rand
5. (3 points) Use Fourier Motzkin Method (not software) to solve the
following question:
Max 5x +y
s.t. 5x +2y S14
y 23
x+3y S 13
36,322 0
Step 1: Let 2=5x+y.
Step 2: Eliminate x:
2 +32 514 y 514-2
y 23 i.e., y 23
z+l4y < 65 l4y<65-z
2,372 0 2,322 0
Step
2. [10 points] Let X have a geometric distribution with parameter 39. Its
probability mass function is
px(r)=(1p)t1p, i=1,2,3,.
(a) Using the above probability mass function, Show that X has the
following z-transform.
GX(z)=1_(f:W IZI <1/(1p).
(b) Use the
3. [10 points] When the production of the transistors is under statistical
quality control about 2% of the transistors are going to be defective.
Suppose that a transistor will be defective independently of the defec-
tive status of the other transistors.
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The Lagrangen is the same as in the paper, except it becomes piecewise as described
by (2a) and (2b).
The rst order conditions
1. [10 points]
(a) We want P(N(1) 2 4) = 1 23:0 cfw_es/51).
b Let X be the number of news a ers sold on a articular da . Its
P l3 p 3
probability mass function is
P(N(1) = 0) = e_3(3/01) J: 0
P(N(1) = 2) = e_3(31/11), :r 2
mm) : Pom) : 2) : 5382/21), x e
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Exercise 5.3.4: Consider a discrete random variable X whose probabil-
ity generating function is given by
GX(2)=ezie+272.
Observe that when 2 = 1, Gx(z) = 1. Find the probabilities px(0), px(1), px(2), px(3),
and px(4)
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Suggested Exercises - Chapter 5
Exercise 5.3.3: Let X be a discrete random variable with probability
mass function given by
1/10, x = 1
2/10, 59 = 2
px(a:) = 3/10, 55' = 3
4/10, 55 = 4
0, otherwise.
Find the probability generat
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Question 1
In the part of the article that is provided for this assignment, limitation of the paper is
not discussed in details. The paper assumes that the residential consumers are not
affected by the
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Suggested Exercises
Probability Axioms
1. Consider the following sample space 9 = cfw_(1, 6, ad, e. Is .7: a a-eld,
where
.7: = cfw_[3, cfw_(L, b, cfw_a, cfw_b, cfw_c, cfw_C,d,, cfw_51, b, 0,151, e?
2. Let Q be a sample s
9 9 T A A E GD) &
> runif(5)
[1] 0. 69424382 0. 03661395 0.32462651 0. 67352867 048179223
Use the inverse transformation technique to convert this sample into a
random sample from an exponential distribution with rate A = 0.1.
Let X have an exponential di