IEOR 162
Homework 3
Linear Programs & Network Flows - Page 1 of 6 Out: September 7, 2016
Due: September 16, 2016
1. The shaded region of the graph below represents the feasible region of a maximization linear
programming problem.
Use the graph to answer t
Department of Industrial Engineering & Operations Research
IEOR 162 Linear Programming and Network Flows (Fall 2016)
1
1.1
Linear programming modeling examples
Investment problem
You own $1 on Monday and want to invest it to maximize the amount on Friday.
Department of Industrial Engineering & Operations Research
IEOR 162: Linear Programming and Network Flows (Fall 2016)
Example of an LP with Multiple Optimal Solutions
Maximize
60x1 + 35x2 + 20x3
subject to
8x1 + 6x2
x3
48
4x1 + 2x2 + 1.5x3
20
2x1 + 1.5x2
IEOR 162
Homework 5
Linear Programs & Network Flows - Page 1 of 6Out: September 22, 2016
Due: September 30, 2016
1. (10 points) Recall the following problem from Homework 2: Consider a window company with
only three employees which makes two different kin
Department of Industrial Engineering & Operations Research
IEOR 162: Linear Programming & Network Flows (Fall 2016)
Manpower planning
Certain types of facilities operate seven days each week and face the problem of allocating person power
during the week
IEOR 162
Homework 1
Linear Programming & Network Flows - Page 1 of 2 Out: August 24, 2016
Due: September 2, 2016
1. A medical equipment company produces a piece of diagnostic equipment at two factories. Three
medical centers have placed orders for this mo
Problem 4
Suppose that a butcher must determine the quantities of ingredients that should be used in making
100 pounds of sausage. The table below provides the requirements and cost information.
Fat
Protein
Water
% of total weight
Cost per Pound
Percentag
Department of Industrial Engineering & Operations Research
IEOR 162: Linear Programming & Network Flows (Fall 2016)
1
Leasing of warehouse space problem
A firm has discovered that its own warehouses will not be sufficient to meet its space requirements
ov
Local vs. Global Optima
Defn: Let x be a feasible solution, then
x is a global max if f(x) f(y) for every feasible y.
x is a local max if f(x) f(y) for every feasible y
sufficiently close to x (i.e., xj-yj xj+ for all j and
some small ).
z
C
B
z = f(x)
IEOR 162
Homework 8
Linear Programming & Network Flows - Page 1 of 6 Out: October 12, 2016
Due: October 18, 2016 at 4:00pm
Note: This homework is due on Tuesday October 18 at 4.00pm. There will be a
submission box outside 4124 Etcheverry.
1. (10 points) C
IEOR 162
Homework 4
Linear Programs & Network Flows - Page 1 of 10Out: September 16, 2016
Due: September 23, 2016
1. (10 points) The manager of a computer help center needs to determine a shift schedule for
his staff. The center is open from 8am until mid
Department of Industrial Engineering & Operations Research
IEOR 162: Linear Programming and Network Flows (Fall 2016)
Class time & location
Lecture: MW 10-11A, 150 GSPP
Discussion: F 9-10A, 3109 Etcheverry or F 10-11A, 3111 Etcheverry
Instructor
Professor
Department of Industrial Engineering & Operations Research
IEOR 162: Linear Programming and Network Flows (Fall 2015)
Giapettos Woodcarving Problem
A toy soldier sells for $27 and uses $10 worth of raw materials. Each soldier that is manufactured increase
IEOR 162
Homework 4
Linear Programs & Network Flows - Page 1 of 10Out: September 16, 2016
Due: September 23, 2016
1. (10 points) The manager of a computer help center needs to determine a shift schedule for
his staff. The center is open from 8am until mid
IEOR 162
Homework 3
Linear Programs & Network Flows - Page 1 of 2 Out: September 7, 2016
Due: September 16, 2016
1. The shaded region of the graph below represents the feasible region of a maximization linear
programming problem.
Use the graph to answer t
Department of Industrial Engineering & Operations Research
IEOR 162: Linear Programming & Network Flows (Fall 2016)
1
An investment problem
An investor has money-making activities A and B available each year for the next 5 years. Each dollar
invested in A
IEOR 162
Homework 6
Linear Programs & Network Flows - Page 1 of 2Out: September 29, 2016
Due: October 7, 2016
1. (10 points) While solving a standard form maximization problem, we arrive at the following
tableau with x3 , x4 and x5 being the basic variabl
IEOR 162
Homework 5
Linear Programs & Network Flows - Page 1 of 2Out: September 22, 2016
Due: September 30, 2016
1. (10 points) Recall the following problem from Homework 2: Consider a window company with
only three employees which makes two different kin
IEOR 162
Homework 7
Linear Programs & Network Flows - Page 1 of 1
Out: October 5, 2016
Due: October 14, 2016
1. (10 points) Use the Big M method and the simplex algorithm to solve the following problem.
State the optimal solution and optimal value of the
Department of Industrial Engineering & Operations Research
IEOR 162: Linear Programming and Network Flows (Fall 2016)
Homework 0
Due: Friday, August 26th
This assignment will be graded but will not count for credit.
In your answers be sure to clearly defi
IEOR 162
Homework 1
Linear Programming & Network Flows - Page 1 of 5 Out: August 26, 2016
Due: September 2, 2016
1. A medical equipment company produces a piece of diagnostic equipment at two factories. Three
medical centers have placed orders for this mo
IEOR 162
Homework 6
Linear Programs & Network Flows - Page 1 of 2Out: September 29, 2016
Due: October 7, 2016
1. (10 points) While solving a standard form maximization problem, we arrive at the following
tableau with x3 , x4 and x5 being the basic variabl
IEOR 162 Linear Programming (Fall 2016)
Quiz, Sep 19th, 2016
Professor Dorit Hochbaum
Name: SID
You have 20 minutes to complete this quiz (the quiz will count for 1% on your nal grade). Good luck!
Question 1. Consider the following linear program.
m
IEOR 162
Homework 4
Linear Programs & Network Flows - Page 1 of 10 Out: February 10, 2016
Due: February 19, 2016
1. (10 points) The manager of a computer help center needs to determine a shift schedule for
his staff. The center is open from 8am until midn
IEOR 162
Homework 2
Linear Programs & Network Flows - Page 1 of 8
Out: January 27, 2016
Due: February 5, 2016
1. A manager of an oil refinery has 8 million barrels of crude oil A and 5 million barrels of crude
oil B allocated for production during the com