(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
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 a
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
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
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
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
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
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 jus
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 ju
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 befor
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
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
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
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 +
(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 t
(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 denit
(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 =
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 vect