MA107: Quantitative Methods (Mathematics)
Solutions to the examination (2016)
Question 1.
(a) As supply is determined by the equation p 3q = 2 we have
q S (p) =
p2
3
and
pS (q) = 2 + 3q,
whereas since
MA107: Quantitative Methods (Mathematics) 201516
Answers for Exercises 9: Linear equations and inverse matrices
Exercise 1. Information about matrix operations and how to solve systems of linear equat
MA107: Quantitative Methods (Mathematics) 201516
Solutions for Extra Exercises 7: Stationary points and Lagrangeans
Extra Exercise 1. The first-order partial derivatives of the function are
fx = 9x2 +
MA107: Quantitative Methods (Mathematics) 201516
Solutions to sample examination question 1
(a) The recurrence equation
2yt 3yt1 + 1 = 0
and to solve this, because a =
which is given by
3
2
can be rew
MA107: Quantitative Methods (Mathematics) 201516
Exercises 9: Linear equations and inverse matrices
For all homeworks in this course please note that no marks will be given for answers only. Always
sh
MA107: Quantitative Methods (Mathematics) 201516
Exercises 10: Integration and Differential equations
For all homeworks in this course please note that no marks will be given for answers only. Always
MA107: Quantitative Methods (Mathematics) 201516
Sample examination question 1
Advice: Read the question, take a look at your notes and then, having put your notes away, do the
question. To get maximu
MA107: Quantitative Methods (Mathematics) 201516
Solutions for Exercises 8: Consumer choice; vectors and matrices
Exercise 1. For information about contours and their gradients see section 12.3 of the
MA107: Quantitative Methods (Mathematics) 201516
Solutions for Exercises 6: Partial derivatives
Exercise 1. By now, the rules of dierentiation should be more or less known. If not, see sections
6.2 an
MA107: Quantitative Methods (Mathematics) 201516
Answers for Extra Exercises 9: Linear equations and inverses
Extra Exercise 1. The augmented matrix describing the equations is
1
2
1
0
2
3
5
1
5
1
4
MA107: Quantitative Methods (Mathematics) 201516
Solutions for Exercises 7: Stationary points and Lagrangeans
Exercise 1. Finding and classifying the stationary (or critical) points of a function of t
MA107: Quantitative Methods (Mathematics) 201516
Answers for Exercises 10: Integration and Differential equations
Exercise 1. The basic ideas and meaning of integration can be found in chapter 25 of t
MA107: Quantitative Methods (Mathematics) 201516
Answers for Extra Exercises 10: Integration and Differential eqns
Extra Exercise 1. For (a), to show that the required algebraic identity holds, we not
MA107: Quantitative Methods (Mathematics) 201516
Exercises 8: Consumer choice; vectors and matrices
For all homeworks in this course please note that no marks will be given for answers only. Always
sh
MA107: Quantitative Methods (Mathematics) 201516
Exercises 2: Sets, functions, graphs, equations
For all homeworks in this course please note that no marks will be given for answers only. Always
show
MA107: Quantitative Methods (Mathematics) 201516
Exercises 7: Stationary points and Lagrangeans
For all homeworks in this course please note that no marks will be given for answers only. Always
show t
Introduction to Calculus
Volume II
by J.H. Heinbockel
The regular solids or regular polyhedra are solid geometric figures with the same identical
regular
polygon on each face.
There are only five regu
MA212: Further Mathematical Methods (Linear Algebra) 201617
Solutions to Exercises 10: Generalised inverses and Fourier series
This document contains answers to the exercises. There may well be some e
MG211.1: Solutions for Chapter 4
4.1 Setting up a new TV channel for TV station CCB involves a number of activities.
These are identified below, together with the cost per day for each activity (in 00
MG211.1: Solutions for Chapter 7
7.1. Revisit Exercise 1.4: What is the expected number of times you have to roll a die
to get a 6? Solve the problem by using Markov chains.
Solution. Let us first def
MG211.1 OPERATIONAL
RESEARCH TECHNIQUES
Lecture 1
Introduction
Course logistics & content
History of OR
Depts of Mathematics & Management
Applications of OR today
Office hours: Fri 14:30-16:30pm
Dr Ls
MG211.1: Solutions for Chapter 5
5.1. A consumer who purchases one of two brands of soap powder every week is influenced
by her choice of the previous week but not by earlier experience. If she purcha
MG211.1: Solutions for Chapter 3
In the solutions we provide the full description of Dijkstras algorithm in every step
using tables as in the lecture notes. You do not need to use this format on the e
MG211.1: Solutions for Chapter 2
1. As in the notes we use n to denote the number of men (and women).
For part a), each woman will receive only one proposal in the first iteration, since
the most pref
MA107: Quantitative Methods (Mathematics) 201617
Solutions for Exercises 5: Optimisation
Exercise 1. This question is similar to worked examples 8.1 and 8.2 of the Anthony & Biggs book.
(a) We are giv
MA107: Quantitative Methods (Mathematics) 201617
Solutions for Exercises 3: Recurrence equations and limits
Exercise 1. Excise tax is discussed in section 1.4 of the Anthony & Biggs book. See also wor
MA107: Quantitative Methods (Mathematics) 201617
Solutions for Exercises 4: The cobweb model and derivatives
Exercise 1. See worked example 4.3 of the Anthony & Biggs book. Given a principal, P , inve
MA107: Quantitative Methods (Mathematics) 201617
Solutions for Exercises 6: Partial derivatives
Exercise 1. By now, the rules of differentiation should be more or less known. If not, see sections
6.2