Due Date: Oct31, Monday – between 9 & 11 AM in room S 2.132 Please keep a copy of your assignment and show all your work clearly.

(1) Mr. J. Bond, a retired movie actor, consumes only grapes and the composite good Y (i.e. price of Y is £1). His income consists of £10000 a year from his investment fund plus the proceeds of whatever he sells of the 2000 bushels of grapes he harvests annually from his vineyard in Tuscany. Last year, grapes sold at £2 per bushel and Bond consumed all 2000 bushels of his grapes, in addition to 10,000 units of Y. This year, the price of grapes is £3 per bushel (and the price of the composite good Y is the same as before). If Bond has well-behaved preferences, will his consumption of grapes this year be greater than, less than or the same as last year’s? How about his consumption of the composite good? (Hint: Graph both years’ budget constraints and think about whether last year’s bundle is affordable to Mr. R).

(2) Suppose Carmela’s income is £100 per week, which she allocates between sandwiches and books. Sandwiches cost £2 each. Books cost £10 each if she purchases between 1 and 5 books. If she purchases more than 5 books in a week, the price falls to £5 for the 6th book and all subsequent books. Draw the budget constraint. Is it possible that Carmela might have more than one utility-maximizing solution?

(3) Fiona requires a minimum level of consumption, to derive additional utility. For Fiona, U(X,Y) = 0 if X+Y<5
= X+Y otherwise.
Which of our usual assumptions about well-behaved preferences are violated in Fiona’s case?

(4) Consider the following utility functions over goods A and B. U = AB, and V = A2B. Compute the MRS for each of these functions, and evaluate these at the point (3,4). Explain whether these functions represent the same preference ordering....

...NATIONAL BOARD FOR HIGHER MATHEMATICS
AND
HOMI BHABHA CENTRE FOR SCIENCE EDUCATION
TATA INSTITUTE OF FUNDAMENTAL RESEARCH
Pre-REGIONAL MATHEMATICAL OLYMPIAD, 2013
Mumbai Region
October 20, 2013
QUESTION PAPER SET: A
• There are 20 questions in this question paper. Each question carries 5 marks.
• Answer all questions.
• Time allotted: 2 hours.
QUESTIONS
1. What is the smallest positive integer k such that k(33 + 43 + 53 ) = an for some positive
integers a and n, with n > 1?
n
√
2. Let Sn =
k=0
1
√ . What is the value of
k+1+ k
99
1
?
n=1 Sn + Sn−1
3. It is given that the equation x2 + ax + 20 = 0 has integer roots. What is the sum of all
possible values of a?
4. Three points X, Y, Z are on a striaght line such that XY = 10 and XZ = 3. What is the
product of all possible values of Y Z?
5. There are n − 1 red balls, n green balls and n + 1 blue balls in a bag. The number of ways of
choosing two balls from the bag that have different colours is 299. What is the value of n?
6. Let S(M ) denote the sum of the digits of a positive integer M written in base 10. Let N be
the smallest positive integer such that S(N ) = 2013. What is the value of S(5N + 2013)?
7. Let Akbar and Birbal together have n marbles, where n > 0.
Akbar says to Birbal, “ If I give you some marbles then you will have twice as many marbles
as I will have.” Birbal says to Akbar, “ If I give you some marbles then you will have thrice
as many marbles as I will have.”
What is the minimum...

...“Problems Encountered by Irregular Students on their Academic Subjects”
Chapter 1
Introduction to the Study
Students encounters many and different problems during their school years. These problems vary differently during their study years. It could be as simple as missing a homework or getting late in class. Or it could be as severe as getting dropped in a certain subject or worse failed the subject.
Several of theseproblems occurs which results for a student to have an irregular status in school. Irregular students are those who have enrolled subjects that are different from regular students. They tend to have a different class schedule compared to regular students. This could mean that they have to cope-up with the time and classmates they would encounter in every class which could give more peer pressure for them. It is not easy for irregular students to have a very complicated class schedule just to enroll subjects they need and to be with different type of people in every class. For some students, it would be difficult to approach new faces in every class and it would be tiring to have a busy class schedule with hardly any vacant time in between class period.
Irregular students often encounter many problems on their academic subjects. The quality of problem can be labeled as severe to a simple type of problem encountered. Failing grades or being...

...of Rough
Set in Soft Set:
A Topological Approach
Tutut Herawan, Universiti Malaysia Pahang, Malaysia
ABSTRACT
In this paper, the author presents the concept of topological space that must be used to show a relation between rough set and soft set. There are two main results presented; firstly, a construction of a quasi-discrete
topology using indiscernibility (equivalence) relation in rough set theory is described. Secondly, the paper
describes that a “general” topology is a special case of soft set. Hence, it is concluded that every rough set
can be considered as a soft set.
Keywords:
Indiscernibility Relation, Quasi Discrete, Rough Set Theory, Soft Set Theory, Topological
Space
1. INTRODUCTION
The problem of imprecise knowledge has been
tackled for a long time by mathematicians. Recently it became also a crucial issue for computer
scientists, particularly in the area of artificial
intelligence. There are many approaches to the
problem of how to understand and manipulate
imprecise knowledge. The most successful one
is, no doubt, the fuzzy set theory proposed by
Zadeh (1965). The basic tools of the theory are
possibility measures. There is extensive literature on fuzzy logic with also discusses some of
the problem with this theory. The basic...

...A STUDY ON PROBLEMS AND PROSPECTS OF GARMENT INDUSTRY
AT TIRUPUR DISTRICT
1. Name of the company
2. Type of ownership (please tick respective one)
a) Solo partnership [ ] b) Partnership [ ]
c) Pvt ltd company [ ] d) Public limited company [ ] e) others [ ]
3. Are you focusing on: - [ ] export / [ ] domestic market [ ] both
4. How long you engage in garment industry
a) Below 5 yrs [ ] b) 5 yrs – 10 yrs [ ]
c) 10 yrs – 15 yrs [ ] d) 15 yrs - 20 yrs [ ] e) more than 20 yrs [ ]
5. Is it is your family business
a) Yes [ ] b) no [ ]
6. Do you agree education is the c2riteria for doing business in
Tirupur city?
a) Strongly agree [ ] b) Agree [ ]
c) No answer [ ] d) Disagree[ ] e) Strongly disagree [ ]
7. What is your annual turnover of the business? _________
8. Rank your strength of business
a) Labor cost advantage [ ] b) Skilled labor availability [ ]
c) Infrastructure [ ] d) availability in raw materials [ ] e) capability in product development [ ]
9. Rank the factor that you find problem in doing business?
a) Cost of finance [ ] b) government tariff [ ] c) In adequate labor [ ]
d) Dying factory problem (pollution control rules by gov) [ ] e) lack of professionalism [ ]
10. Please rank, based on aspect of opportunities
a) 1 [ ] b) 2 [ ] c) 3 [ ] d) 4 [ ] e) 5 [ ]
11. Are...

...Amazing Grace School
San Vicente, San Pedro, Laguna
Problems Encountered by 3rd Year and 4th Year Students of
Amazing Grace School while Selecting Course in
College this SY 2011-2012
By:
Acupan, Cheyanne Kleir T.
Amuan, Mark Benjamin D.G.
Galang, Allan Gerold M.
Manalo, John Daniel T.
Pinpin, Jose Maria Emmanuellee
Remoquillo, Katrina L.
To, Efraim Julian M.
2011-2012
A Partial Requirement for Graduation in High School SY 2011-2012
Introduction
Various problems are now being experienced by our country and there are a lot of things that brought changes to our lives. Socio-economic problems, bureaucratic problems, and the biggest problem faced by our country, financial problem, are greatly affected by global economic crisis. As students, we are hoping that someday we will be the one to bring hope to this country, don’t be one of the burdens to it and help it progress and attain its ultimate success, and the beginning of that vision would start with the right choice of college course. With that proper choice of course, we will be able to develop and improve our God given talents and apply our knowledge and intelligence to it, though it is a free of cost opportunity to select and pick a course, this is not an easy task for it requires a lot of analysis of the course and decision-making. During the period of our childhood, we always have reveries of what...

...
Identifying Barriers Experienced by Human Service Clients
XXXXXXX X XXXXXXXX
April 7, 2010
BSHS/305
Professor Bill Eady
Problems Facing Human Services Clients
Human service professionals have a very rewarding career. They are given the opportunity in more ways than one to provide help to those who are in need of it. While this profession can be rewarding, unfortunately, this area of expertise can be emotionally exhausting because of the many problems that the human service clients face and the lack of resources that are available to them. These problems include, but are not limited to, economic inequality, poverty, child welfare as well as social problems.
While these problems are evident daily, human service professionals are trained to notice the oppression and social injustice and to develop solutions to the problems so they will not continue to persist in the future (France, 2005). For example, human service professionals are more aware of the common denominator or factor that is present among a family living in poverty, an incarcerated individual and a person living with a disability. The single factor that is common from this example would be a lack of resources due to their social identities. While it is the goal of human service professionals to promote social equality for all, unfortunately, living in today’s society, this is...

...-------------------------------------------------
Set (mathematics)
From Wikipedia, the free encyclopedia
This article is about what mathematicians call "intuitive" or "naive" set theory. For a more detailed account, see Naive set theory. For a rigorous modern axiomatic treatment of sets, see Set theory.
An example of a Venn diagram
The intersection of two sets is made up with the objects contained in both sets
In mathematics, a set is a collection of distinct objects, considered as an object in its own right. For example, the numbers 2, 4, and 6 are distinct objects when considered separately, but when they are considered collectively they form a single set of size three, written {2,4,6}. Sets are one of the most fundamental concepts in mathematics. Developed at the end of the 19th century, set theory is now a ubiquitous part of mathematics, and can be used as a foundation from which nearly all of mathematics can be derived. In mathematics education, elementary topics such as Venn diagrams are taught at a young age, while more advanced concepts are taught as part of a university degree.
-------------------------------------------------
Definition[edit]
A set is a well defined collection of objects. The objects that make up a set (also known as the elements or members of a...

...Essay 1
Set And Subset of Assemblages
Devanshi Purohit
Each assemblage is an emergent entity which can combine with others to produce ever larger assemblages; both assemblages and their component parts are thus characterized by reciprocal relations of exteriority (Parr, 2005). This statement poses a question that whether it can be considered that each assemblage is made up of smaller assemblages as well as there is a larger universal assemblage that each assemblage is a part of.
Robert Beauregard's essay, In Search of Assemblages, suggests how assemblage thinking can be one applicable planning approach. "Most importantly, they(assemblages) are also practically useful; if properly constituted, assemblages contain all of the actors(and forces) relevant for the design of a planning intervention." (Beauregard). It can be considered that the city is made of multiple partially localized assemblages built of heterogeneous networks, spaces, and practices. Similarly, assemblage thinking can also be applied to scrutinize complexities in social, political, cultural and spatial systems. Moreover, Actor-Network theory being one of the theoretical perspectives that led to assemblage thinking. This theory suggests the subjectivity of each actor that is the part of an assemblage and that the actions of each actor are dependent of the other actors and factors of the network. Consequently, the same actor may or may not play the same role in different networks....