ENS208 - 2011-2012 Fall
Recitation 10 Questions
Question 1.
Leary Chemical manufactures three chemicals: A, B and C. These chemicals are produced via
two production processes: 1 and 2. Running process 1 for an hour costs $4 and yields 3 units
of A, 1 of B
ENS 208 - Fall 2011
Homework 5 Solutions
Question 1. (Problem 4.12 on page 201, Nahmias 5th Ed.)
A large automobile repair shop installs about 1250 mufflers per year, 18 percent of which are
for imported cars. All the imported-car mufflers are purchased f
Chapter 5 - Examples
Example 1 (Problem 5.8 on page 248, Nahmias 5th Ed.)
Billys bakery bakes fresh bagels each morning. The daily demand for bagels is a random
variable with a distribution estimated from prior experience given by
# of bagels
sold in one
Quiz-3
1.
y=3
1/4
0
0
1/8
y=2
0
1/8
1/4
0
y=1
0
0
1/8
1/8
x=1
x=2
x=3
x=4
x, y
Tablodan (joint PMF) faydalanarak:
a. px(x) ve py(y) yi bulunuz.
b. pxy(xy)yi bulunuz.
c. p(x|1<y<x)i bulunuz.
2. A,B ve C adnda olaymz olsun. Bu olaylar hakknda aadaki bilgile
ENS208 - 2011-2012 Fall
Recitation 13 Questions
Question 1. (Problem 4.10 on page 201, Nahmias 5th Ed.)
A specialty coffeehouse sells Columbian coffee at a fairly steady rate of 280 pounds annually.
The beans are purchased from a local supplier for $2.40
ENS 208 - Fall 2012
Homework 3 Solutions
Question 1. A local semiconductor firm, Superchip, is planning its workforce and production
levels over the next year. The firm makes a variety of microprocessors and uses sales dollars as
its aggregate production
Winter's Exponential Smoothing results for HW2
Alpha =
Beta =
Gamma =
Apr 2011
May 2011
Jun 2011
July 2011
Aug 2011
0.39
0.28
0.94
Note that these parameters are usually desired to be small for
stable forecasts.
Date Observation Level Trend Season Forecas
ENS 208
Homework 1 Solutions
Fall 2012
Q1. Calculate the stress and strain induced on a cylindrical bar (made of AISI 4340 steel having
50 mm diameter and 2 m long) which is under 5000 N of tensile force. Will the bar yield under
this loading condition? (
ENS 208 - Fall 2011
Homework 5,
Due on January 5, 2012, 15.30
This assignment will be carried out individually.
You can submit your paperwork to the box near FENS 1021.
Question 1. (Problem 4.12 on page 201, Nahmias 5th Ed.)
A large automobile repair shop
ENS 208 - Fall 2011
Homework 4 Solutions
Question 1.
Identify the special case of the following LP by the help of graphical solution method.
max
z = x1 + x 2
s.t.
x1 + x 2 4
x1 x 2 >= 5
x1 , x 2 0
Solution
AB is x1 + x2 = 4. CD is x1 - x2 = 5. From graph
ENS 208 - Fall 2011
Homework 4,
Due on December 27, 2011, 15.30
This assignment will be carried out individually. You can either submit your paperwork to
the box near FENS 1021 or upload the relevant files to SUCourse for questions 1-2.
Question 1.
Identi
ENS208 - 2011-2012 Fall
Recitation 1 Questions
Q1. A 1000 kg 4-wheel drive BMW is traveling up 30 inclined road at a speed of 108 km/h.
The friction coefficient between the wheels and road is 0.5.The diameter of the tires is 400
mm. What is the power and
ENS208 - 2011-2012 Fall
Recitation 2 Questions
Q1. Consider a plain carbon steel with the following properties:
Ultimate Tensile Strength
UTS (MPa)
Yield Strength
y (MPa)
620
Youngs Modulus
E (GPa)
Shear Modulus
G (GPa)
Poissons Ratio
Strain Hardening Ex
ENS208 - 2011-2012 Fall
Recitation 3 Questions
Q1. Derive an expression for the toughness of a material represented by the equation
= K ( + 0.2 )n and whose fracture strain is denoted as f .
Q2. Take two solid cylindrical specimens of equal diameter but
ENS208 - 2011-2012Fall
Recitation 4Questions
Q1:
200 mm
Rigid
z
1
2
100 mm
30000 N force is applied at the midpoint of
the horizontal rigid bar along +z direction.
Bars 1 and 2 are fixed on the ground. It is
given that the bars 1 and 2 have the following
1. Let X be a random variable with PMF( X PMFi aadaki gibi olan bir rasgele
deikendir)
x 2 / a,
p X ( x)
0,
x 3, 2, 1, 0,1, 2, 3,
otherwise
if
a) Find a and E[X].
( a ve E[X] bulunuz)
b) Compute the variance of X using Z=(X-E[X])2
(Xin varyansn Z=(X-E[X
ENS 208
Introduction to
Manufacturing Systems
Inventory Control Subject to
Uncertain Demand
by Blent atay Sabanci University
The Nature of Uncertainty
Suppose that we represent demand as
D = Ddeterministic + Drandom
If the random component is small compa
ENS 208
Introduction to
Manufacturing Systems
Inventory Control Subject to
Known Demand
by Blent atay Sabanci University
Types of Inventories
Raw materials
Resources required in production or processing activity
Components
Items that have not been comple
A
1
2
3
4
5
6
7
8
9
10
11
12
13
14
32
33
50
51
B
C
Beginning Inventory
End of Inventory
Cost of a worker/day
Hiring cost/worker
Firing cost/worker
Holding cost/unit - month
K = # of items /worker-day = 8000/(174*46)
Current# of workers for chase & level s
A
1
2
3
4
5
6
7
8
9
10
11
12
13
14
32
33
50
51
B
C
Beginning Inventory
End of Inventory
Cost of a worker/day
Hiring cost/worker
Firing cost/worker
Holding cost/unit - month
K = # of items /worker-day
Current# of workers for chase & level strategies
Curren
ENS208 - 2011-2012 Fall
Recitation 8 Question
ABC Company needs to plan workforces and production levels for the six-month period of
January to June to produce the famous ABC game consoles. The following table shows
forecasted demand for the game consoles
Sales3
Example 3
Month
Jan 2008
Feb 2008
Mar 2008
Apr 2008
May 2008
Jun 2008
Jul 2008
Aug 2008
Sep 2008
Oct 2008
Nov 2008
Dec 2008
Jan 2009
Feb 2009
Mar 2009
Apr 2009
May 2009
Jun 2009
Jul 2009
Aug 2009
Sep 2009
Oct 2009
Nov 2009
Dec 2009
Jan 2010
Feb 201
Sales3
Example 3
Month
Jan 2007
Feb 2007
Mar 2007
Apr 2007
May 2007
Jun 2007
Jul 2007
Aug 2007
Sep 2007
Oct 2007
Nov 2007
Dec 2007
Jan 2008
Feb 2008
Mar 2008
Apr 2008
May 2008
Jun 2008
Jul 2008
Aug 2008
Sep 2008
Oct 2008
Nov 2008
Dec 2008
Jan 2009
Feb 200
Sales3
Example 3
Month
Jan 2008
Feb 2008
Mar 2008
Apr 2008
May 2008
Jun 2008
Jul 2008
Aug 2008
Sep 2008
Oct 2008
Nov 2008
Dec 2008
Jan 2009
Feb 2009
Mar 2009
Apr 2009
May 2009
Jun 2009
Jul 2009
Aug 2009
Sep 2009
Oct 2009
Nov 2009
Dec 2009
Jan 2010
Feb 201