1. Write the decision variables in the short form2. Write the objective function3. Write the constraints and domain condition 48. The city hall wants to rehabilitate a rural area of 25,000 m2 next to the townin order to allocate a recreation area. There are several options with differentcosts of construction and maintenance, required space, and expected users. Thisinformation is given in the following table:FacilityFootball 7 fieldClay tenniscourtNormal tenniscourt1st paddlecourt2nd paddlecourtSports pavilionLarge picnicareaSmall picnicareaInitial cost Annual maintenance(thousands cost (thousands ofof €)€)120880650302020025154332521Required space(m²)2.5001.2001.2004003003.00020.00010.000Expectedusers8005004003002001.3001.2001.000The city hall has a grant of 250,000€ for the rehabilitation, and 30,000€ of eachyear's budget for the maintenance. Decide which facilities should be chosen inorder to maximize the number of expected users, considering that the tenniscourts and the picnic areas are incompatible, while the second paddle court canbe built only if the first one is built.

The city hall aims to rehabilitate a rural area adjacent to the town and transform it into a…

Answered: 1. Write the decision variables in the…

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

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

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.

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