OPMT 5701
Constrained Optimization: Lagrange Method
SHORT ANSWER: Show your steps & identify the rules you use.
1) Use the method of Lagrange multipliers to determine the critical points of f(x, y) = 4x2 + 2
y2 + 3 subject to the constraint x+ 2y = 9.
1)

OPMT 5701
BBA program
Homework 2: Lines and Quadratic Equations
Review Section 2.1 of Jacques (6th ed)
Note: Vertex means "top or bottom"
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
1) (a) Sketch the

Question 5 from Matrix Study Questions
A group of investors has $500,000 to invest in the stocks of three companies.
Company A sells for $50 a share and has an expected growth of 13% per year.
Company B sells for $20 per share and has an expected growth o

OPMT 5701:
Assignment 8:
Differential and implicit differentiation
Read Chapters 5.1, 5.2 & appendix 2. Also the web-notes on differentials and
Implicit function theorem
Questions 1 to 12 involve using the method of differentials. Sometimes you will need

OPMT 5701
Maximum and Minimum for two variable functions.
Review your notes on Unconstrained Optimization.
From The text read chapter 5.4 and Apendix 3 (Hessians)
SHORT ANSWER. Solve the following problems. In each case, clearly write out the First Order

OPMT 5701: Derivatives of ln(x) ex
1) Find y' if y = ln(2x 2 - 3).
2) Find y' if y = ln
Remember: ln(AB) = lnA + lnB
x-1
.
x+1
3) Find y' if y = ln (x 2 + 5)5 (3 - 4x) 4 .
4) Find y' if y = x 3 ln(4x + 5).
5) If y =
ln x
, then find y'.
ln x 2
6) If y = l

OPMT 5701 Homework 6 One Variable Optimization
ANSWER KEY
1. If f (x) = 2x3 + 3x2 36x + 1, determine the intervals on which f is increasing and the
intervals on which f is decreasing
f 0 = 6x2 + 6x 36
= 6(x2 + x 6)
f 0 = 6(x + 3)(x 2)
Function is increasi

OPMT 5701
Homework #7
Partial Derivatives
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
1) If f(x, y) = 4x 3 y 2 + 3x 2 y 4 - 7xy2 + 4x - 3y + 2, find (a) f x (x, y) and (b) f y (x, y).
1)
2) Find
f
f
a

OPMT 5701 Midterm
Winter 2014
NAME:
Tuesday Night Section
ID # :
Total:
/15
PART II: Three Questions 5 marks each (15 marks)
1. If f (x) = 22
1 3
3x
+ 5x2
16x
(a) nd all the critical points and determine whether they are relative maximums or minimums.
f 0

OPMT 5701
Homework # 1
Note: The answers were generated using Maple 8.0.
Red is the commands; Blue is the solution, Black is text
> with(linalg):
Warning, the protected names norm and trace have been redefined and
unprotected
Question 1:
y + 2
x
=
x + y

OPMT 5701 Homework: Finding the Inverse
Name_
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
1) Let A = 1 2 ; find A-1.
3 4
1)
2) (a) If A is the coefficient matrix of the system x + 3y = 2 , determine A

OPMT 5701,
Fall 2009
Multiple Constraints
Homework 11
1. Consider the case of a two-good world where both goods, x and y. are rationed. Let the consumer,
Myrtle, have the utility function U = U (x; y). Myrtle has a xed money budget of B and faces the
mone

OPMT 5701 Term Project 2013
Selected Answers
1. Willingness to Pay versus Equivalent Compensation
Skippy and Myrtle are friends who consume the same goods: yoga classes (X) and Timbits (Y ).
Skippy has the utility function u = u(x; y) and faces the budget

OPMT 5701
Pre-Calculus Review
Name_
No Calculators are Permitted
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
1) Completely factor: 3ax + 9ay
1)
2) Completely factor: x2 - 36
2)
3) Completely factor: x

Linear equations 1
Name_
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
1) Find the slope of the line passing through the points (5, -3) and (2, -1).
1)
2) For the line y = 7x - 3, find (a) the slope and

OPMT 5701
Additional Constrained Optimization Problems
ANSWER KEY
Due: November 24, 2010
Instructions: Below are some additional applications of the lagrange method. Show all your work. These
problems are due in lab
1. Maximize
u = 4x2 + 3xy + 6y 2
subjec