AmericanUniversityofBeirutFEA
EngineeringManagementProgram
Fall2010ENMG500:EngineeringManagementI
Prof.A.Yassine
HomeworkSet8&9
Problem 1:
In inter-modal transportation, loaded truck trailers are shipped between railroad terminals by placing the trailer o

GE288
Homework 12
Reading Assignment: Section 20.1 of Taha.
1. Problem 1, set 20.1A, p. 705 of Taha.
2. Problem 2, set 20.1A, p. 705 of Taha.
3. Problem 3, set 20.1A, p. 705 of Taha.
4. Prove part (1) of Theorem 20-1.3 on p. 704 of Taha.
Fall 02

GE288
Homework 8
Fall 02
Reading Assignment: Sections 6.1, 6.2, 6.3 (only Dijkstras algorithm, not Floyds
algorithm). The formulation of some of these problems can be tricky. So please try
to do all the exercises in the book, in addition to the homework a

GE288
Homework 11
Fall 02
Reading Assignment: Section 9.2.1 of Taha.
1. Problem 4, p. 379, problem set 9.2A of Taha. (Just graphically verify infeasibility, you
dont have to use the B&B method.)
2. Problem 5, p. 379, problem set 9.2A of Taha.

GE288
Homework 9
Fall 02
Reading Assignment: Section 6.4 (excluding 6.4.4) of Taha.
Notes:
1. The second mid-term exam will be held from 7 p.m. to 9 p.m. on Monday,
November 11 in Room 114 TB (the room where we meet for class.)
2. The mid-term will cover

GE288
Homework 10
Fall 02
Reading Assignment: Section 9.1 of Taha.
1. Explain how the following conditions can be represented as linear constraints using 0-1
variables:
(i)
Either x+y 2 or 2x+3y 8
(ii)
Variable z can assume values 0, 5, 9 and 12 only.
(ii

Final Exam Topics
Everything covered in class and all the homework assignments. These include:
LPs:
Formulation
Interpreting Excel output and sensitivity analysis
Graphical solution and sensitivity analysis
Tableau method: standard form, identifying enter

GE288
Homework 3
Fall 02
1. Consider Problem 1, problem set 2.3 A, page 25 of Taha. For parts (a), (b) and (c),
suppose that the objective is changed to c1x1+c2x2. Find conditions on c1 and c2 such that
the optimal solution remains unchanged.
2. Consider

GE288
Homework 2
Fall 02
1. Solve the following problem graphically:
max 2a+3b
s.t.
a4
b4
a+2b 10
a 0, b 0
Clearly mark the feasible region and show how you varied the objective function (2a+3b)
to get the optimal solution. Clearly write out the optimal s

GE288
Homework 1
Fall 02
1. A machine shop has one drill press and five milling machines, which are to be used to produce
an assembly consisting of two parts, 1 and 2. The productivity of each machine for the two parts
is given below:
Production time in m

GE288
Homework 13
Fall 2002
1. Consider the problem
Max -2x2+4x-3y2+48y-10
subject to
4x+6y=14.
(a) Solve the problem.
(b) Find the optimal profit.
(b) Without solving the problem again, estimate the change in the optimal value of the
objective if the rig

GE288
Homework 5
Fall 02
Notes:
1. Class will be cancelled on Oct. 2 and Oct. 4.
2. Office Hours will be cancelled on Oct. 2 and Oct. 3.
3. Quiz 5 will be held on Monday, Oct. 7 in class.
4. I will hold office hours from 2:00-3:00 on Tuesday, Oct. 8 and W

GE288
Homework 7
Fall 02
Reading Assignment: Sections 5.2 and 5.3 (excluding 5.3.3 and 5.3.4)
Note: In class, we calculate c-(u+v) and pick the unused cell with the smallest (most
negative) value of c-(u+v) to enter. The book computes (u+v)-c and picks th

GE288
Homework 6
Fall 02
Reading Assignment:
Notes on duality, available on the course home page.
Sections 5.1 and 5.2 of Taha.
1. Problem 4, Problem set 4.1A, page 119 of Taha.
2. Problem 4, Problem set 5.2A, page 175 of Taha. Formulate (do not solve)