Engineering Optimization ISyE 3833 - Quiz 2 - Solution
1. A metallurgy company makes two grades of bronze: high grade and low grade. Both types
of bronze are made by mixing copper and tin. High grade bronze must be between 70%
and 85% copper (by weight),
Problem Set 2 - Solutions
Linear Programming
1. Solution:
In this problem we have 4 types of possible suppliers (Abundo (A), Colmado (C), Maximo (M),
and Saboro (S) which we can buy, and also 3 types of coee (Hotel (H), Restaurant (R), Market
(M) that we
Extra Practice Problems for Exam 2
1. For each of the following problems, do the following:
Graph the feasible region (if it exists)
Determine if the feasible region is bounded or unbounded
Solve the LP graphically
If there exists multiple optimal sol
ISyE 3833: Engineering Optimization
October 4, 2015
Solution Midterm 1 - 2015
Lecturer: Santanu S. Dey
Scribe: Santana, A.
Question 1 My company assembles electronic parts and sells the assembled nal products.
1. We sell two nal products. Selling price of
ISyE 3833: Engineering Optimization
September 22, 2015
Lecture 11
Lecturer: Santanu S. Dey
1
Scribe: Santana, A.
XOR variables
Given
x1 =
1 if decision 1 is taken
0 otherwise
x2 =
1 if decision 2 is taken
0 otherwise,
we want to model:
x3 =
1 exactly one
ISyE 3833: Engineering Optimization
September 17, 2015
Lecture 10
Lecturer: Santanu S. Dey
1
Scribe: Santana, A.
Fixed Cost
1.1
An Investment Problem
Solution:
Variables:
xi : equals 1 if production occurs in month i, and equals 0 otherwise, i cfw_1, , 6;
ISyE 3833: Engineering Optimization
September 15, 2015
Lecture 9
Lecturer: Santanu S. Dey
1
Scribe: Santana, A.
If-Then Constraints
We want to model the following kind of problem.
I need to manufacture cars such that:
1. the total number of cars is at mos
ISyE 3833, HW 3 Solutions
1. Beerco manufactures ale and beer from corn, hops, and malt. At present, 40 lb of corn, 30 lb of
hops, and 40 lb of malt are available. A barrel of ale sells for $40 and requires 1 lb of corn, 1 lb of
hops, and 2 lb of malt. A
ISyE 3833, HW2 Solutions
1. Solve the following LPs using the simplex method (by hand). Clearly say in your solution if you
reached an optimal solution or detected that the LP is unbounded.
(a)
max
2x1 + 3x2 + 4x3
s.t.
x1 + x2 + x3 5
2x1 + x2 + 2x3 10
x1
ISyE 3833, HW1 Solutions
1. Either state that
1 2
A = 2 1
3 3
the matrix is not invertible or find the inverse of
2
0
2
Solution:
Note that the rows R1 , R2 , R3 of A are linearly dependent, specifically
1
2
3
R1 + R2 R3 = 2 + 1 3 = 0
2
0
2
and so the
ISyE 3833 - HW 3
Due: Mar 16 / 17
Solve the following LPs using the simplex algorithm. Use the two-phase simplex algorithm when
appropriate. If the LP has an optimal solution, state it, and state the optimal value. Otherwise,
state clearly whether the LP
ISyE 3833 - HW 1
Due: Jan 27 / 28
1. (From Winston, Section 2.1, Problem 1) For
1 2 3
A= 4 5 6
7 8 9
find:
1 2
B = 0 1
1 2
and
(a) A,
(e) B T ,
(b) 3A,
(f) AB, and
(c) A + 2B
(g) BA.
(d) AT ,
2. (From Winston, Section 2.1, Problem 2) Only three brands o
Engineering Optimization ISyE 3833 - Quiz 3 SOLUTION
Time: 1 hour
Name:
1. (6 pt) Euing Gas produces two types of gasoline (gas 1 and gas 2) from two types of oil (oil 1
and oil 2). Each gallon of gas 1 must contain at least 50 percent oil 1, and each gal
ISyE 3833: Engineering Optimization
October 4, 2015
Solution Midterm 1 - 2015
Lecturer: Santanu S. Dey
Scribe: Santana, A.
Question 1 My company assembles electronic parts and sells the assembled final products.
1. We sell two final products. Selling pric
Engineering Optimization ISyE 3833 - Quiz 2 - Solution
1. A metallurgy company makes two grades of bronze: high grade and low grade. Both types
of bronze are made by mixing copper and tin. High grade bronze must be between 70%
and 85% copper (by weight),
Engineering Optimization ISyE 3833 - Quiz on IP formulations
Name:
A company is considering opening warehouses in four cities: New York (NY), Los Angeles (LA),
Chicago and Atlanta. Each warehouse can ship 100 units per week. The weekly fixed cost of
keepi
ISYE 3133, Fall 2012
Homework 3 Solutions
April 27, 2014
1. I f x is the number of cars produced then we want: If x > 0 then x + 50 0, so
that:
x 500y
x + 50 500(1 y)
For y cfw_0, 1. Note that x + 50 50(1 y) also works here as the second constraint.
7. Le
ISyE 3833: Engineering Optimization
September 10, 2015
Lecture 8
Lecturer: Santanu S. Dey
1
Scribe: Santana, A.
Scheduling
Solution:
Variables:
xi : number of nurses beginning on day i, for all i cfw_1, 2, , 7
Individual variables restrictions:
For all i
ISyE 3833: Engineering Optimization
September 8, 2015
Lecture 7
Lecturer: Santanu S. Dey
Scribe: Santana, A.
In this lecture we do one more linear program formulation and then we move on to
integer formulation problems.
1
Min Max Formulations
Next is anot
ISyE 3833: Engineering Optimization
September 3, 2015
Lecture 6
Lecturer: Santanu S. Dey
Scribe: Santana, A.
From now on we will start doing some more complex formulations, for instance, in some
cases we will have to use auxiliary variables as in the next
Engineering Optimization ISyE 3833, Fall 2016 - Quiz 2
Name:
1. (10 points) The FASET leaders need a certain number of t-shirts to give to incoming
students during each of the next 4 weeks of FASET sessions. The number of shirts
needed in week j is dj for
ISyE 3833 - HW 3
Due October 12/13
Solve the following LPs using the simplex algorithm. If the LP has an optimal solution, state it,
and state the optimal value. State clearly if the simplex method reveals that the LP is unbounded.
1.
max 2x1 + x2 3x3 + 5
Name:
Section:
ISyE 3833: Engineering Optimization
Midterm 1
March 10th, 2016
1:35pm to 2:50pm
Remarks.
This is a closed book exam.
No calculators.
There are 4 problems in total.
Write your name on every sheet.
Row:
1
Name:
Problem 1.
Section:
Row:
2
ISyE 3133
Summer 2016
Exam 2
07/19/16
Time Limit: 105 Minutes
Name (Print):
Signature:
GTID:
Instruction:
This exam contains 10 pages (including this cover page) and 5 problems (including one for extra
credit). Check to see if any pages are missing. Ente