You have been assigned to arrange the songs on the cassette version of the famous music band, Nirvana’s latest album. A cassette tape has two sides (1 and 2). The songs on each side of the cassette must total between 14 and 16 minutes in length. The length and type of each song are given in the table below. The assignment of songs to the tape must satisfy the following conditions. Song Type Length (in minutes) 1 Ballad 4 2 Hit 5 3 Ballad 3 4 Hit 2 5 Ballad 4 6 Hit 3 7 5 8 Ballad and hit 4 Formulate the problem as an IP to determine which song is assigned to which side of the cassette to satisfy the following conditions. a) The songs on each side of the cassette must total between 14 and 16 minutes in length. b) Each song must be assigned to exactly either one of the sides. c) Each side must have exactly two ballads. d) Side 1 must have at least 3 hit songs. e) Either song 5 or song 6 must be on side 1. f) If song 2 and 4 are on side 1, then song 5 must be on side 2.
You have been assigned to arrange the songs on the cassette version of the famous music band, Nirvana’s latest album. A cassette tape has two sides (1 and 2). The songs on each side of the cassette must total between 14 and 16 minutes in length. The length and type of each song are given in the table below. The assignment of songs to the tape must satisfy the following conditions.
|
Song |
Type |
Length (in minutes) |
|
1 |
Ballad |
4 |
|
2 |
Hit |
5 |
|
3 |
Ballad |
3 |
|
4 |
Hit |
2 |
|
5 |
Ballad |
4 |
|
6 |
Hit |
3 |
|
7 |
|
5 |
|
8 |
Ballad and hit |
4 |
Formulate the problem as an IP to determine which song is assigned to which side of the
cassette to satisfy the following conditions.
a) The songs on each side of the cassette must total between 14 and 16 minutes in
length.
b) Each song must be assigned to exactly either one of the sides.
c) Each side must have exactly two ballads.
d) Side 1 must have at least 3 hit songs.
e) Either song 5 or song 6 must be on side 1.
f) If song 2 and 4 are on side 1, then song 5 must be on side 2.
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