Answers to Homework 2 Problems
Dr. Jaya Singhal
1. The Charm City Bakery makes coffee cakes and Danish pastries in large pans. The main
ingredients are flour and sugar. There are 25 pounds of flour and 16 pounds of sugar available.
The demand for coffee c

Linear Programming: Graphical Methods for Minimization Problems
And Special Situations
Dr. Jaya Singhal
Graphical Methods for Minimization LP Problems
A minimization LP problem can be solved by using a graphical method IF it contains only two
variables. T

Decision Analysis
Decision analysis models deal with the situations in which a decision maker must make decisions
based on uncertain future conditions. For example, the demand for a Christmas time product is
based on the economic conditions at Christmas t

Integer Programming
Dr. Jaya Singhal
Like linear programming, integer programming also consists of objective function, constraints,
and non-negativity constraints, but it also contains the additional constraints of one or more
variables must be integers.

Transportation and Assignment Problems
This week, we will learn how to build and solve mathematical models for some special linear and
integer applications: transportation problem and assignment problem. As the names imply, these
models deal with transpor

Review of Linear Algebra
Variable: A variable is a mathematical symbol capable of taking one of the many
possible values. Given a linear equation or a linear inequality, the values of variables in it
are not known. The goal, usually, is to solve the equat

Queuing Analysis
We have all waited in queues at some time or other, be it in a supermarket checkout line, at a gas
pump, in a bank, to receive a flu shot, or at a red light. Waiting in lines is an everyday occurrence.
For a person waiting in line, the pr

Queuing Analysis
We have all waited in queues at some time or other, be it in a supermarket checkout line, at a gas
pump, in a bank, to receive a flu shot, or at a red light. Waiting in lines is an everyday occurrence.
For a person waiting in line, the pr

LP: Sensitivity Analysis
Dr. Jaya Singhal
The parameters in a linear programming problem change with time because of changes in market
conditions, technological advances, availability of material and labor, etc. Sensitivity analysis is
useful in determini

Linear Programming: Introduction
And Graphical Methods for Maximization Problems
Dr. Jaya Singhal
Introduction to Linear Programming
Linear programming is a special technique in decision sciences. It can be applied to a large number of
real world business

LP: Computer Solution
Dr. Jaya Singhal
It is not possible to solve a linear programming problem with more than two variables by using
the graphical method. If a linear programming problem has more than two variables then we must
use an algebraic method (t

Linear Programming Applications
Dr. Jaya Singhal
The main objective of this course is to apply the methods learnt in this course to appropriate real
world situations. This is done by first building a mathematical model, second solving it by using a
comput

Answers to Midterm Exam 2 Questions
Answer Questions 2 and 3 based on the following LP problem.
Maximize 10X1 + 15X2 + 20X3
Total Profit
Subject to
X1 + X2 + X3 > 200
At least a total of 200 units of all three products needed
X1 + 3X2 + 2X3 500
Resource 1

Answers to Midterm Exam 1 Questions
2. Given the following linear programming problem
Maximize 6x + 5y
Subject to
x + y < 80
3x + y < 120
2x + y > 20
x, y > 0
(a) Graph the constraints.
(b) Find the coordinates of each corner point of the feasible region

OPRE 315: Homework 4 Answers
1. A manufacturing company produces diesel engines in four factories located in Phoenix, Seattle,
Baltimore, and Detroit. Three trucking firms purchase these engines for their plants located in
Greensboro, Miami, and Charlesto

Answers to Homework 3 Problems
Dr. Jaya Singhal
1. The Charm City Air Conditioning manufactures four home air conditioners: an economy model, a
regular model, a super model, and a luxury model. The profits per unit are $50, $70, $120, and $140,
respective

Answers to Homework 1 Problems
Dr. Jaya Singhal
1. An investment company has 20 million dollars to invest this year. Currently, the company is
considering different ways to invest the money. Their objective is to have maximum return on the
investment. Wha