61. A water theme park plays seven games depending on the demand during weekdays and weekends. The park earns revenues (in thousands of euros) from playing these games and the revenue varies with the days. Certain games generate more revenue during weekends and certain games do not yield any revenue. The park analyzed its revenue data and prepared a revenue matrix as follows (values in euros): Games Monday Tuesday Wednesday Thursday Friday Saturday Sunday A 2 2 0 3 8 7 4 B 2 0 0 3 5 5 5 C 2 0 0 3 7 4 5 D 0 0 0 2 8 5 6 E 0 0 1 0 5 8 8 F 0 0 1 0 6 4 8 G 0 2 1 3 5 4 8 Besides, the machines used for these games require maintenance and have other costs associated with them. The park realizes the games F and G can be played at most 2 times a week; while all other games can be played up to three times a week. On any given day, a game cannot be played more than once. The park also plans to play a maximum of 2 games daily from Monday through Thursday to amuse the few visitors during weekdays. During the weekend (Friday, Saturday, and PROBLEMS 199 Sunday), to amuse the large number of visitors, the park plays a maximum of 5 games. The park wants to know which game should be played on which days to maximize revenue. a. Formulate a linear programming model for this problem. b. Solve this model using computer. c. If the park plans to play all seven games during weekends, what will be its revenue? d. If the park considers customers' ranking (analogously called weights) of games instead of costs and maximizes the ranking while satisfying constraints, how does the solution change? In a study conducted over a week, customers ranked the games as follows. (1: the least liked; 7: the most liked) Games Monday Tuesday Wednesday Thursday Friday Saturday Sunday A 1 4 7 1 6 7 1 B 7 3 6 2 7 6 2 с 2 2 5 3 1 1 3 D 3 1 1 7 2 2 7 E 6 5 2 6 3 3 6 F 5 6 3 5 4 4 5 G 4 7 4 4 5 5 4
61. A water theme park plays seven games depending on the demand during weekdays and weekends. The park earns revenues (in thousands of euros) from playing these games and the revenue varies with the days. Certain games generate more revenue during weekends and certain games do not yield any revenue. The park analyzed its revenue data and prepared a revenue matrix as follows (values in euros): Games Monday Tuesday Wednesday Thursday Friday Saturday Sunday A 2 2 0 3 8 7 4 B 2 0 0 3 5 5 5 C 2 0 0 3 7 4 5 D 0 0 0 2 8 5 6 E 0 0 1 0 5 8 8 F 0 0 1 0 6 4 8 G 0 2 1 3 5 4 8 Besides, the machines used for these games require maintenance and have other costs associated with them. The park realizes the games F and G can be played at most 2 times a week; while all other games can be played up to three times a week. On any given day, a game cannot be played more than once. The park also plans to play a maximum of 2 games daily from Monday through Thursday to amuse the few visitors during weekdays. During the weekend (Friday, Saturday, and PROBLEMS 199 Sunday), to amuse the large number of visitors, the park plays a maximum of 5 games. The park wants to know which game should be played on which days to maximize revenue. a. Formulate a linear programming model for this problem. b. Solve this model using computer. c. If the park plans to play all seven games during weekends, what will be its revenue? d. If the park considers customers' ranking (analogously called weights) of games instead of costs and maximizes the ranking while satisfying constraints, how does the solution change? In a study conducted over a week, customers ranked the games as follows. (1: the least liked; 7: the most liked) Games Monday Tuesday Wednesday Thursday Friday Saturday Sunday A 1 4 7 1 6 7 1 B 7 3 6 2 7 6 2 с 2 2 5 3 1 1 3 D 3 1 1 7 2 2 7 E 6 5 2 6 3 3 6 F 5 6 3 5 4 4 5 G 4 7 4 4 5 5 4
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.4: Applications
Problem 28EQ
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Transcribed Image Text:61. A water theme park plays seven games depending on the demand during weekdays and weekends.
The park earns revenues (in thousands of euros) from playing these games and the revenue varies
with the days. Certain games generate more revenue during weekends and certain games do not
yield any revenue. The park analyzed its revenue data and prepared a revenue matrix as follows
(values in euros):
Games Monday Tuesday Wednesday Thursday Friday Saturday Sunday
A
2
2
0
3
8
7
4
B
2
0
0
3
5
5
5
C
2
0
0
3
7
4
5
D
0
0
0
2
8
5
6
E
0
0
1
0
5
8
8
F
0
0
1
0
6
4
8
G
0
2
1
3
5
4
8
Besides, the machines used for these games require maintenance and have other costs associated
with them. The park realizes the games F and G can be played at most 2 times a week; while all
other games can be played up to three times a week. On any given day, a game cannot be played
more than once. The park also plans to play a maximum of 2 games daily from Monday through
Thursday to amuse the few visitors during weekdays. During the weekend (Friday, Saturday, and
PROBLEMS
199
Sunday), to amuse the large number of visitors, the park plays a maximum of 5 games. The park
wants to know which game should be played on which days to maximize revenue.
a. Formulate a linear programming model for this problem.
b. Solve this model using computer.
c. If the park plans to play all seven games during weekends, what will be its revenue?
d. If the park considers customers' ranking (analogously called weights) of games instead of
costs and maximizes the ranking while satisfying constraints, how does the solution change?
In a study conducted over a week, customers ranked the games as follows. (1: the least liked;
7: the most liked)
Games Monday Tuesday Wednesday Thursday Friday Saturday Sunday
A
1
4
7
1
6
7
1
B
7
3
6
2
7
6
2
с
2
2
5
3
1
1
3
D
3
1
1
7
2
2
7
E
6
5
2
6
3
3
6
F
5
6
3
5
4
4
5
G
4
7
4
4
5
5
4
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