Quantitative Methods
MAT 540
Simulation
1
Objectives
Upon completion of this lesson, you will
be able to:
Create statistical analysis of
simulation results.
Use technology and information
resources to research issues in
Management Science.
2
What is Si
Microsoft Excel 15.0 Answer Report
Worksheet: [Julia's Food Booth.xlsx]LP (2)
Report Created: 11/22/2015 9:42:42 AM
Result: Solver found a solution. All Constraints and optimality conditions are satisfied.
Solver Engine
Engine: Simplex LP
Solution Time: 0
Hoylake Rescue Squad
Probability of Time between calls
P(x)
0.15
0.1
0.2
0.25
0.2
0.1
1
Cumulative
(lower
Time between
bound)
calls
1
2
3
4
5
6
EV =
Average Time =
Simulation
simulation
Number
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
RN
Time
Cum
Cab Company Scheduling
let Di = # of drivers who start their 8 hour shift in period I (I = 1,2,3,4,5,6)
period 1
12:00:00 AM4:00am
period 4
12 noon  4:00pm
period 2
4:00am  8:00am
period 5
4:00pm  8:00pm
period 3
8:00am  12 noon
period 6
8:00pm  mid
(a) Define the decision variables and write the linear programming model for the pro
x1=rice
cost:
.03x1+06x2
x2=oats
Vit A
6x1+10x2>=45
Vit B
3x1+2x2>=13
(b) Sketch the feasible region. Give your answer in the worksheet named P1Graph
(i) You can use QM
P1
1. transportation problem
From
A
B
C
DV
From
A
B
C
Constraint
Demand
Objective
1
$6
11
4
To (cost)
2
$5
8
10
3
$5
9
7
1
0.00
0.00
70.00
70.00
=
70
To
2
125.00
85.00
0.00
210.00
=
100
3
25.00
0.00
55.00
80.00
=
80
Minimize Cost $2,095.00
Page 1
Constrai
ENGINEERING ANALYSIS I
4600:260003
Spring, 2017 QUIZ 4
ID#_ NAME _
(50 pts) Please manually convert the base16 number
to a base8
number. The first 16 numbers table is given below, for your reference. Please show
your work.
Binary
Octal Decimal Hexadeci
ENGINEERING ANALYSIS I
4600:260003
Spring, 2017 QUIZ 5
ID#_ NAME _
(50 pts) Find out the value (magnitude expressed in base 10 number) of the
following double precision floating point number which is represented in IEEE
format. Please show your work.
000
Engineering Analysis I: 4600:260003
Spring, 2017 IC7 (Group)
Due: 2/23 (required)
1. The following infinite series can be used to approximate :
= + +
+ + +
!
!
a) Prove that this Maclaurin series expansion is a special case of the Taylor series
(Eq.
Engineering Analysis I: 4600:260003
ID#
Name (print)
Spring, 2017 IC9 (Group)
Due: 3/16 (required)
Signature
1. Given the system of equations
(a) Compute the determinant.
(b) Use Cramers rule to solve for the s.
(c) Use Gauss elimination to solve for the
Why does government exist?
Natural theory:
The nature of human beginnings requires some for of governance; Seeks
it through family units
Humans are by nature social creatures and require ourselves to have structure and interact with
each other in a politi
SLGP Notes Wed 27 January 2016
Magna Carta: King of England needed money so he traded rights for money for nobles.
British kicked out the King during English civil war King was brought back following war
Created the premise for parliament to rule along si
Adam BenPorath
Week 1 Weekly Activity
A governments function is to establish a system of rules and laws in which people must
abide by to create a stable state, and to protect its citizens. People abide by these laws and give
up certain rights in exchange
SLGP Notes Wed 2/17/16
Executive Branch Continued
Attorney General: Mike DeWine elected 2010 & 2014
Chief Official in state in regards to legal matters
Office was not created until 1846 as an appointed positon
After constitution revap in 1851 became elect
Article 2: The Presidency
Article 2 Is supposed to define the executive branch but focuses entirely on the presidency.
Describes the process of election of the president and defines some enumerated powers.
There is vagueness because the constitution does
Mechanical Engineering, Fund Of Mechanical VIbrations
UNKNOWN 431

Summer 2008
e forces developed in the Viscous Ganiptzss acting u .
iiif 2.23 Draw a FED showing th
I Label the forces in terms of 9.
bar of Figure Si2.23 at an arbitrary instant.
FiGURE SP 2.23;
Describe the equivalent systems method.
When are static spring f
Mechanical Engineering, Fund Of Mechanical VIbrations
UNKNOWN 431

Summer 2008
2.23 Draw a FBD showing he forces from the viscous dampers. Label the forces in terms of the time
derivative of the chosen generalized coordinate
&
2.34 Determine the equivalent mass or
equivalent moment of inertia of the system
shown in Figure 2.34 when
Mechanical Engineering, Fund Of Mechanical VIbrations
UNKNOWN 431

Summer 2008
Homework Set 4
Short answer questions
EA
3.41 n= mL
JG
3.42 n= IL
48 EI
3.43 n= m L3
Chapter Problems
2.48 Derive the differential equation governing the motion of onedegreeoffreedom system by
applying the appropriate form(s) of Newtons laws to the app
Mechanical Engineering, Fund Of Mechanical VIbrations
UNKNOWN 431

Summer 2008
Introduction
nouns mg
1.10 For the system shown in Figure PLIO, the angular dispiacement of the thin
disk is given by 60) = 0.03 sin cfw_30: + 475) rad. The disk tolls Without slipping
on the surface. Determine the Following as functions of time.
(a) Th
Mechanical Engineering, Fund Of Mechanical VIbrations
UNKNOWN 431

Summer 2008
Problems from book for HW Set 5
3.33 The damping ratio of the system of Figure P3.33 is 0.3. How long will it take for the
amplitude of free oscillation to be reduced to 2% of its initial value?
3.42 The initial recoil velocity of a 1.4kg gun is 2.5 m/s.
Mechanical Engineering, Fund Of Mechanical VIbrations
UNKNOWN 431

Summer 2008
Vibrations HW Set 5
Spring 2016
Dr. S.G. Kelly
Due February 27, 2017
Chapter problems from textbook
3.33, 3.42 ,3.43
1. The free vibrations of a SDOF system are governed by the differential equation
5&
x& 100 x& 1400 x 0
(a)
(b)
(c)
(d)
What is the system
Mechanical Engineering, Fund Of Mechanical VIbrations
UNKNOWN 431

Summer 2008
4600:431/531 Fundamentals of Mechanical Vibrations
HW Set 2
Short answer problems
x= 1
Given: F = 300 N
F
300 N
k=
=
=3 10 5 N /m
.
x 0.001 m
2.30
2.31
Given:
F=300
mm.
x= 1
N
The
mm.
stiffness
The
of
the
potential
element
is
energy
is
2
1
1
V = k ( x
Mechanical Engineering, Fund Of Mechanical VIbrations
UNKNOWN 431

Summer 2008
4600:431/531 Fundamentals of Mechanical Vibrations
HW Set 3
Due February 13, 2017
Short answer problem from text
2.23 At an arbitrary instant the upper bar has rotated through an angle , measured positive
clockwise. The lower bar has an angular displaceme
Mechanical Engineering, Fund Of Mechanical VIbrations
UNKNOWN 431

Summer 2008
4600:431/531 Fundamentals of Mechanical Vibrations
HW Set 3
Due February 13, 2017
Short answer problems from text
2.23
Chapter problems
2.34, 2.43, 2.48, 2.53
1. What is the energy dissipated between
t0
and
t 1
sec by a viscous damper of damping
coefficie
Mechanical Engineering, Fund Of Mechanical VIbrations
UNKNOWN 431

Summer 2008
HW Set 5
Book Problems
3.33 The damping ratio of the system of Figure P3.33 is 0.3. How long will it take for the
amplitude of free oscillation to be reduced to 2% of its initial value?
Given: = 0.3, k = 2 103 N/m,
m = 4.2 kg,
L = 1.1 m
Find: t for X = 0.
Mechanical Engineering, Fund Of Mechanical VIbrations
UNKNOWN 431

Summer 2008
4600:431/531 Fundamentals of Mechanical Vibrations
HW Set 2
Short answer problems
2.30, 2.31, 2.33, 2.35
Chapter problems
2.2, 2.9, 2.10, 2.19
Not from the book problems
1. How many degrees of freedom are necessary to model the system illustrated below. S
Mechanical Engineering, Fund Of Mechanical VIbrations
UNKNOWN 431

Summer 2008
4600:431/531 Fundamentals of Mechanical Vibrations
Homework Set 1
Due January 30, 2017
Chapter problems (from text)
1.10, 1.12, 1.18, 1.27, 2.2, 2.9
Problems not from text
1. The 0.6 kg uniform rigid bar is pinned at A. At the instant shown the rigid body
Mechanical Engineering, Fund Of Mechanical VIbrations
UNKNOWN 431

Summer 2008
HW Set 4 Book Problems
2.48 Derive the differential equation governing the motion of onedegreeoffreedom system by
applying the appropriate form(s) of Newtons laws to the appropriate freebody diagrams. Use
the generalized coordinate shown in Figure P2.