ENCE360
Spring 2020
Homework No. 4
Problem 1
You have been assigned to arrange the songs on the cassette version of Taylor’s latest album.
A cassette tape has two sides (side 1 and side 2). The songs on each side of the cassette must
total between 14 and 16 minutes in length and type of each song are given in the following
table. The assignment of songs to the tape must satisfy the following conditions:
1.
Each side must have exactly two ballads.
2.
Side 1 must have at least three hit songs.
3.
Either song 5 or song 6 must be on side 1.
4.
If songs 2 and 4 are on side 1, then song 5 must be on side 2.
Explain how you could use an integer programming formulation to determine whether
there is an arrangement of songs satisfying these restrictions.
Song
Type
Length (in minute)
1
Ballad
2
Hit
3
Ballad
4
Hit
5
Ballad
6
Hit
7
8
Ballad and Hit
Problem 2
Five projects are being evaluated over a 3-year planning horizon. The following table gives
the expected returns for each project and the associated yearly expenditures.
a)
Formulate an IP which helps in identifying the projects which should be selected over
the 3-year planning horizon.
b)
Modify the formulation such that project 5 must be selected if either project 1 or
project 3 is selected.
c)
Modify the formulation such that projects 2 and 3 are mutually exclusive.
4
5
3
2
4
3
5
4

ENCE360
Spring 2020
Homework No. 4
Problem 3
Dorian Auto is considering manufacturing three types of auto: compact, midsize, and large.
The resource required for, and the profits yielded by, each type of car is shown in the
following table. At present, 6000 tons of steel and 60000 hours of labor are available. In order
for production of a type of car to be economically feasible, at least 1000 cars of that type must
be produced. Formulate an IP to maximize Dorian’s profit.
Compact
Midsize
Large
Steel required
1.5 tons