CO 250 Assignment 1 Fall 2012
Due: Friday September 21 at 10:30 a.m.
Total marks: 40
Solutions are due in the CS drop box 3.These boxes are the PINK boxes on the 3rd oor of the MC
building, by the elevators and the bridge to DC (and NOT across from the tu
Assignment 1 Corporate Finance II (ACTSC372)
Due date: Feb 4, 5:00pm. Outside MC 6016 _
1. Consider the following two stocks: Expected Return
30% 19%
Beta Murck Pharmaceutical Pizer Drug Corp
1.4 0.7
Assume that capital asset pricing model holds. Based on
CO 250 Introduction to Optimization Fall 2012 Solutions to Assignment 8
1. [ (2+2+2) + 2 = 8 marks]
a)
i) Observe that for the edge sb,
slacky (sb) = csb ycfw_s ycfw_s,a ycfw_s,a,c = 2 1 1 1 = 1.
Since slacky (sb) < 0, the given y is not feasible.
ii) The
CO 250 Introduction to Optimization Fall 2012 Solutions to Assignment 6
1. [6 marks] Without loss of generality, we can assume that (P ) is in canonical form for B , so
that the constraints read as
xB +
x i Ai = b
iN
where N = cfw_1, . . . , n \ B . Lets
CO 250 Introduction to Optimization Fall 2012 Solutions to Assignment 5
1. [18 marks = 14 + 4]
(a)
i. This is not in canonical form because c3 > 0. One can use the formula to get it into
canonical form, but one can predict what it will do: essentially sub
CO 250 Introduction to Optimization Fall 2012 Solutions to Assignment 1
1. Academic Integrity. [3 marks = 1+1+1]
(a) The main oences are Cheating, Plagiarism, Unauthorized collaboration, Misrepresentation and Impersonation.
(b) Plagiarism is taking someon
AMath 350
Assignment #2
Fall 2012
due Wednesday, September 26th
Hand in #2, 5, 6, and 7.
1. Are the following equations separable, linear, neither, or both?
a)
b)
c)
d)
e)
f)
2.
dy
= y + ex
dx
dy
= ex sin( y )
dx
dy
= 5y 2
dx
dy
= x y2
dx
dy
x2
=y
dx
dy
y
AMath 350
Assignment #2
Fall 2011
SOLUTIONS
1. (Are the given equations separable, linear, neither, or both?)
a) Not separable, but linear.
b) Separable, but non linear.
c) Both.
d) Neither.
e) Both.
f) Separable, but not linear.
2.
a) Find the general so
Review Questions
Test 1 - HRM 200
Spring 2013
Define discrimination?
What are two types of discrimination?
What is reasonable accommodation?
What is undue hardship?
What is a BFOR?
Define Harassment?
What are two types of sexual
harassment?
What s
Sample Interview Question
There are many types of interview questions and some of them are dedicated to reflect a
certain aspect of the interviewees. For example, the interviewer can ask the question,
"what was the name of company, position title and desc
AMath 350
Assignment #3
Fall 2012
Solutions
1.
dy
+ 3xy = 1. Find the solution if y (1) = 1,
dx
and state its interval of existence.)
dy 3
1
Solution: This is linear. In standard form it is
+ y = 2.
dx x
x
R3
dx
3 ln x
3
x
An integrating factor is e
=e
=x
AMath 350
Assignment #3
Fall 2012
due Wednesday, October 3rd
Hand in #1, #3, #5, and #6
1.
dy
a) Consider the equation x2 + 3xy = 1. Find the solution if y (1) = 1, and
dx
state its interval of existence.
b) Solve the initial value problem
dy
+ 2xy = 1,
d
AMath 350
Assignment #5
Fall 2011
NOT for submission
1. Solve the following equations, using the variation of parameters method:
1x
e
x
b) y + y = sin (x2 )
a) y 2y + y =
2.
for x > 0
Note:
sec xdx = ln (sec x + tan x) + C
a) Consider the dierential equat
AMath 350
Assignment #4
Fall 2011
Solutions
1.
a) y 00 + y 0 2y = 0
Solution: The characteristic equation is m2 + m 2 = 0, which gives
(m + 2)(m 1) = 0 =) m = 2, 1. Therefore the general solution is
y = c1 e
2x
+ c2 e x .
b) y 00 + 4y 0 + 4y = 0
Solution:
AMath 350
Assignment #4
Fall 2012
due Friday, October 12th
Hand in #2, #3, #5, #6, and #7.
1. Find the general solutions to the following ODEs:
a) y 00 + y 0
2y = 0
b) y 00 + 4y 0 + 4y = 0
c) y 00 + 2y 0 + 5y = 0
d) y 00 + y 0
6 y = 6x
e) y + 3y + 12y 0 +
Dierential Equations
for Business and Economics
Course Notes for AMATH 350
Sue Ann Campbell
Department of Applied Mathematics
University of Waterloo
Fall 2011
c S.A. Campbell 2010
Contents
1 Introduction
1
2 First Order Ordinary Dierential Equations
5
2.1
CO250 Sample Final Exam
Question 1 (12 marks ). Formulation
The company Newmusic needs to set the price $x of each item downloaded. They wish
to maximize the prot, which is calculated as total price of all items sold per hour. Market research indicates th
1. LP formulation [12 marks]
CO Toasters needs to produce 1000 units of their new toaster model. There are three ways this toaster can
be produced: manually, semi-automatically, and robotically. Manual assembly requires 1 minute of skilled
labour, 40 minu
CO 250 Assignment 5 Fall 2012
Due: Friday October 19 at 10:30 a.m.
Total marks: 30.
Solutions are due in the CS drop box 3 (3rd oor of the MC building, by the elevators
and the bridge to DC) by the due time. Use the appropriate slot for your section and
s
CO 250 Assignment 3 Fall 2012
Due: Friday October 5 at 10:30 a.m.
Total marks: 50.
Solutions are due in the CS drop box 3 (3rd oor of the MC building, by the elevators and the
bridge to DC) by the due time. Use the appropriate slot for your section and su
C O250 I NTRODUCTION TO O PTIMIZATION - P RACTICE A SSIGNMENT 4 SOLUTIONS
Exercise 1 (10 marks).
(a) No, since the columns cfw_1, 2, 5 do not form an identity matrix (they are the right columns but the wrong
order by the denitions in this course, canonica
C O250 I NTRODUCTION TO O PTIMIZATION - A SSIGNMENT 4 ( PRACTICE ONLY !)
Do not hand this assignment in. It is for practice only and will not be marked. Solutions will be posted
approx. October 11.
Exercise 1 (10 marks).
The following LP is in SEF:
max
(0
CO 250
Assignment 2
Solutions
Total marks: out of 40 (plus up to 5 bonus)
1. [5 marks]
Solution. Let xij be a 0-1 variable indicating that an X is placed in the (i, j ) position. Then the
number of 1s placed is just 3=1 3=1 xij . This is the objective fun
CO250 ASSIGNMENT 2
Due Friday, 28th September at 10:30 in the drop boxes
CS box 3, slots 3 6 (3rd oor, near the bridge)
Total marks: out of 40 (plus up to 5 bonus)
1. [5 marks] Formulate an IP whose solution gives the answer to the following question:
Wha
ACTSC 371 Corporate Finance 1
Assignment 2 Due Date November 5, 2012 at 3:30 pm
Please submit your assignment in the DROP BOXES outside the math tutorial centre.
Question 1: The annual earnings of Avalanche Skis Inc will be $4 per share in perpetuity if t