ORBS 7010
Operational Research I
Classwork
Name:
Student ID:
Date: 12 September, 2016
Question
In preparation for the winter season, a clothing company is manufacturing parka and goose overcoats,
insulated pants, and gloves. All products are manufactured
EXAMPLE
Toy, Inc., manufactures two types of wooden toys: soldiers and trains. A soldier
sells for $27 and uses $10 worth of raw materials. Each soldier that is
manufactured increases Toys variable labour and overhead costs by $14. A train
sells for $21 a
Consider the linear programming problem,
max =
st =
0
, .
where
A solution of the equation = if basic if at most m of its entries are non-zero,
i.e., if there exists a set cfw_1, , with | = such that = 0 if . The set is
then called basis, and variabl
MORE EXAMPLES ON LINEAR
PROGRAMMING
1
EXAMPLE
Marys diet requires that all the food she eat come from one of the four
basic food groups (chocolate cake, ice cream, soda and cheesecake). At
present, the following four foods are available for consumption: b
Tutorial 1
Question 1
The following is the yearly coffee production (in coded units) of a certain country
from 1991 to 2000.
year
1991
1992
1993
1994
1995
1996
1997
1998
1999
2000
Coffee production
9
11
12
12
14
15
14
16
19
20
(a) Calculate the forecast f
A linear programming problem (LP)
is an optimization problem
for which we do the following:
1 We attempt to maximize (or minimize) a linear function of the decision
variables. The function that is to be maximized or minimized is called the
objective funct
MATH2005 Probability and Statistics for Computer Science
MATH2006 Probability and Statistics for Science
STAT1620 Computer-Aided Statistics
Suggested Answers for Assignment 03
1. (a) df = n 1 = 18 1 = 17, t0.975 = 2.110
2.7
s
= 27 (2.110) = 27 1.343
x t1/
MATH2005 Probability and Statistics for Computer Science
MATH2006 Probability and Statistics for Science
STAT1620 Computer-Aided Statistics
Supplementary Exercise
Instructions:
a. Answer ALL the questions.
b. The full mark is 100.
c. Your answers for the
MATH2005 Probability and Statistics for Computer Science
MATH2006 Probability and Statistics for Science
STAT1620 Computer-Aided Statistics
Suggested Answers for Assignment 04
1. (a) Check n
p = (15)(9/15) = 9 > 5 and n(1 p) = (15)(6/15) = 6 > 5.
s
p z(1/
MATH2005 Probability and Statistics for Computer Science
MATH2006 Probability and Statistics for Science
STAT1620 Computer-Aided Statistics
Supplementary Exercise
Suggested Answers
1. (a) x = 20.1111, s2 = 26.0561, s = 5.1045, = 8, t0.975 = 2.3060
confide
MATH2005 Probability and Statistics for Computer Science
MATH2006 Probability and Statistics for Science
STAT1620 Computer-Aided Statistics
Assignment 4
Due date: 21 April 2016
Instructions:
a. Your answer for the hypothesis test should contain all of the
Inference on Population Proportion
MATH 2005
Probability and Statistics for Computer Science
(MATH 2005)
Inference on Population Proportion
Second Semester 2015
1 / 27
Learning Outcomes
Able to perform hypotheses testing
Able to perform and analyze hypoth
Analysis of Variance
MATH 2005
Probability and Statistics for Computer Science
(MATH 2005)
Analysis of Variance
Second Semester 2015
1 / 18
Learning Outcomes
Identify the principles behinds various statistical methods
Carry out various parameter estimatio
Categorical Data
MATH 2005
Probability and Statistics for Computer Science
(MATH 2005)
Categorical Data
Second Semester 2015
1 / 22
Learning Outcomes
Identify the principles behinds various statistical methods
Carry out various parameter estimations and h
Basic R
MATH 2005
Probability and Statistics for Computer Science
(MATH 2005)
Basic R
Second Semester 2015
1 / 22
Help Information
help(.)
Example
> help(lm)
Fitting Linear Models
Description
lm is used to fit linear models. It can be used to
carry out re
Proof + Code
MATH 2005
Probability and Statistics for Computer Science
2015-2016 Semester 2
Contents
1 Expected Value and Variance for Discrete Random Variable
3
2 Expected Value and Variance for Continuous Random Variable
5
3 Moment Generating Function
7
Hypothesis Testing
MATH 2005
Probability and Statistics for Computer Science
(MATH 2005)
Hypothesis Testing
Second Semester 2015
1 / 46
Learning Outcomes
Identify the principles behinds various statistical methods
Carry out various parameter estimations a
Comparing Two Populations
MATH 2005
Probability and Statistics for Computer Science
(MATH 2005)
Comparing Two Populations
Second Semester 2015
1 / 43
Learning Outcomes
Identify the principles behinds various statistical methods
Carry out various parameter
MATH2005 Probability and Statistics for Computer Science
MATH2006 Probability and Statistics for Science
STAT1620 Computer-Aided Statistics
STAT1210 Probability and Statistics
Suggested Answers of Assignment 1
1. (a) mean: 4, median: 3.5, mode: 1
(b) rang
Suggested Answers of Mid-term Examination
1. (a) XA N (100, 252 )
60 100
)
25
= P (Z 1.6)
P (XA 60) = P (Z
= 0.0548
(b) XB N (75, 152 )
P (XB X1 )
X1 75
)
P (Z
15
X1 75
15
X1
= 0.75
= 0.75
= 0.67
= 85.05
(c)
60 75
)
15
= P (Z 1)
P (XB 60) = P (Z
= 0.15
MATH2005 Probability and Statistics for Computer Science
MATH2006 Probability and Statistics for Science
STAT1620 Computer-Aided Statistics
Suggested Answers of Assignment 2
1. (a) The number of adults selected (X) is geometrically distributed (p = 0.3).
MATH2005 Probability and Statistics for Computer Science
MATH2006 Probability and Statistics for Science
STAT1620 Computer-Aided Statistics
STAT1210 Probability and Statistics
Assignment 1
Due date: 29 Feb 2016
Total marks: 130
1. (34 marks) The U.S. Ener
MATH2005 Probability and Statistics for Computer Science
MATH2006 Probability and Statistics for Science
STAT1620 Computer-Aided Statistics
Mid-term Examination
Student Name:
Student ID Number:
1
Write your answers in the space provided. Total marks: 60.
MATH2005 Probability and Statistics for Computer Science
MATH2006 Probability and Statistics for Science
STAT1620 Computer-Aided Statistics
Assignment 3
Due date: 14 April 2016
Instructions:
a. Your answer for the hypothesis test should contain all of the
MATH2005 Probability and Statistics for Computer Science
MATH2006 Probability and Statistics for Science
STAT1620 Computer-Aided Statistics
Assignment 2
Due date / time: 14 Mar 2016 (9:00am)
Total marks: 160
1. (33 marks) A survey database shows that 30 p