1. Write the decision variables in the short form 2. Write the objective function 3. Write the constraints and domain condition

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Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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1. Write the decision variables in the short form

2. Write the objective function

3. Write the constraints and domain condition

48. The city hall wants to rehabilitate a rural area of 25,000 m2 next to the town
in order to allocate a recreation area. There are several options with different
costs of construction and maintenance, required space, and expected users. This
information is given in the following table:
Facility
Football 7 field
Clay tennis
court
Normal tennis
court
1st paddle
court
2nd paddle
court
Sports pavilion
Large picnic
area
Small picnic
area
Initial cost Annual maintenance
(thousands cost (thousands of
of €)
€)
120
8
80
6
50
30
20
200
25
15
4
3
3
25
2
1
Required space
(m²)
2.500
1.200
1.200
400
300
3.000
20.000
10.000
Expected
users
800
500
400
300
200
1.300
1.200
1.000
The city hall has a grant of 250,000€ for the rehabilitation, and 30,000€ of each
year's budget for the maintenance. Decide which facilities should be chosen in
order to maximize the number of expected users, considering that the tennis
courts and the picnic areas are incompatible, while the second paddle court can
be built only if the first one is built.
Transcribed Image Text:48. The city hall wants to rehabilitate a rural area of 25,000 m2 next to the town in order to allocate a recreation area. There are several options with different costs of construction and maintenance, required space, and expected users. This information is given in the following table: Facility Football 7 field Clay tennis court Normal tennis court 1st paddle court 2nd paddle court Sports pavilion Large picnic area Small picnic area Initial cost Annual maintenance (thousands cost (thousands of of €) €) 120 8 80 6 50 30 20 200 25 15 4 3 3 25 2 1 Required space (m²) 2.500 1.200 1.200 400 300 3.000 20.000 10.000 Expected users 800 500 400 300 200 1.300 1.200 1.000 The city hall has a grant of 250,000€ for the rehabilitation, and 30,000€ of each year's budget for the maintenance. Decide which facilities should be chosen in order to maximize the number of expected users, considering that the tennis courts and the picnic areas are incompatible, while the second paddle court can be built only if the first one is built.
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