(2.1) To prove: 2 = 0 if and only if is a multiple of l. l 1 Proof: Note that 2 = h1 h1 , where h1 = 1 1 l. l 1 l () Suppose 2 = h1 h1 = 0. Since is positive denite, we must have h1 = 0. l 1 1 l. Left-multiplying both sides of the equation by we Therefore

CO 327 - Homework assignment 4
Spring 13
Page 1
CO 327 - Spring 13
Homework assignment #4: (Due at the beginning of the class, 10:00AM, on Tuesday, July
2nd)
Instructions:
Please show all your work and justify your answers. Answers without proper justica

CO 327 - Homework assignment 3
Spring 13
Page 1
CO 327 - Spring 13
Homework assignment #3: (Due at the beginning of the class, 10:00AM, on Thursday, June
6th)
Instructions:
Please show all your work and justify your answers. Answers without proper justic

CO 327 - Homework assignment 5
Spring 13
Page 1
CO 327 - Spring 13
Homework assignment #5: (Due at the beginning of the class, 10:00AM, on Tuesday, July
16th)
Instructions:
Please show all your work and justify your answers. Answers without proper justic

CO 327 - Homework assignment 6
Spring 13
Page 1
CO 327 - Spring 13
Homework assignment #6: (Due never)
Question 1 - 1 (0 points)
A swim coach is putting together a team for the 400m medley relay. The 4 swimmers have the following
times in seconds:
Free Br

CO 327 - Homework assignment 5
Spring 13
Page 1
CO 327 - Spring 13
Homework assignment #5: (Due at the beginning of the class, 10:00AM, on Tuesday, July
16th)
Instructions:
Please show all your work and justify your answers. Answers without proper justic

CO 327 - Homework assignment 2
Spring 13
Page 1
CO 327 - Spring 13
Homework assignment #2: (Due at the beginning of the class, 10:00AM, on Thursday, May
30th)
Instructions:
Please show all your work and justify your answers. Answers without proper justic

CO 227 - Homework assignment 1
Fall 10
Page 1
CO 227 - Fall 10
Homework assignment #1: (Due at the beginning of the class, 10:30AM, on Monday, Oct
4th)
Instructions:
Please show all your work and justify your answers. Answers without proper justication
w

CO 227 - Homework assignment 5
Fall 10
Page 1
CO 227 - Fall 10
Homework assignment #5: (Due at the beginning of the class, 10:30AM, on Friday, Nov
19th)
Instructions:
Please show all your work and justify your answers. Answers without proper justication

CO 327 Final Exam SAMPLE, Spring 2013
Page 1
Question 1 (0 points)
MachineCo is trying to determine its production of products A,B,C,D for the next year. Each product
must pass through a machine before being completed. The typical requirements in terms of

Assignment 1
Due: Wednesday January 22 at the BEGINNING of class
1. This question will test your ability to understand OPL code.
(a) The following is the .mod le for a particular OPL model. Write out the general
structure of the linear program using stand

Assignment 5
Due: Wednesday April 2 at the BEGINNING of class
1. A power plant has two boilers, which produce steam, and two turbines, which produce
power from steam. The following two tables give the specications of the boilers and
the turbines. The rst

Assignment 2
Due: Wednesday February 5 at the BEGINNING of class
1. Example of a Multiperiod Problem: Investing
A person has $21,000 and plans to invest it over the next 3 years. Their nancial advisor has suggested three investments to invest in. Each inv

Assignment 3
Due: Wednesday February 26 at the BEGINNING of class
Consider the given LP of the form maxcfw_cT x | Ax b, x 0:
maximize
120x1 + 200x2 + 400x3
subject to
10x1 + 20x2 + 40x3
25x1 + 30x2 + 50x3
40x1 + 50x2 + 100x3
x
12000
25000
45000
0
For the

(1.2) Rewrite the question in the form 1 min c x + x C x s.t. Ax = b 2 where 400 C = diag (4, 6, 8) = 0 6 0 which is positive denite, 008 c = (0, 0, 0) , A = (2, 3, 4), and b=9 By Theorem 1.3 of the text (rst-order necessary and sucient condition of optim

(5.10a) Consider the problem without nonnegativity constraints, 1 mincfw_t x + x x | l x = 1, 2 whose solution is given by x(t) = h0 + th1 , l 1 1 l and h1 = 1 1 1 l. l 1 l l l Since is positive denite and diagonal, we know that x(0) = h0 > 0. Therefore,

(2.11) The optimality conditions for this problem are t x = ul and l x = 0, which implies that x = u1 l + t1 and 0 = l x = ul 1 l + tl 1 . Therefore, u=t and x = t which has p = x = t h1 = t1 ,
2 p = x x = t2 h1 h1 = t2 2 = t2 1 ,
l 1 l 1 l 1 l + t1 = th1

CO 227 Assignment 5 Solutions
Exercise 3.12
We are given that the rst n constraints have linearly independent gradients, which means
that cfw_a1 , . . . , an are linearly independent. Removing a vector from a linearly independent
set of vectors does not