A community council must decide which recreation facilities to construct in its community. Five new recreation facilities have been proposed - a soccer field (xs), an athletic field (xa), a gymnasium (xg). a swimming pool (xp), a tennis center (xp). The council wants to select facilities that will maximize the expected daily usage by the residents of the community, subject to budget and selection limitations. The expected daily usage and cost information for each facility are given below: Recreation Facility Expected Usage (people/day) Cost (S in K) Soccer field 180 50 Athletic field 130 20 Gymnasium 240 85 Swimming pool 270 40 Tennis center 70 15 The community has a $140K construction budget. The selection must also comply with the following two criteria: (1) At least two of the proposed facilities must be selected; and (2) gymnasium and tennis center cannot be selected simultaneously. Fill in the blanks to complete the formulation for this 0-1 integer programming model that maximizes the expected usage. You should type the missing coefficient values. (Hint: If a variable should not appear in a constraint, then you should type 0 for its coefficient value.) Max Z = 180 xg+ 130 xa + 240 xg + Xp + st. 50 xs + 20 xa + Xg + Xp + 15 x4s 140 1 xg + 1 xg + 1 xg + 1 xXp + 1 x¢2 Xa+ Xg+ Xp+ Xj is binary for all i
A community council must decide which recreation facilities to construct in its community. Five new recreation facilities have been proposed - a soccer field (xs), an athletic field (xa), a gymnasium (xg). a swimming pool (xp), a tennis center (xp). The council wants to select facilities that will maximize the expected daily usage by the residents of the community, subject to budget and selection limitations. The expected daily usage and cost information for each facility are given below: Recreation Facility Expected Usage (people/day) Cost (S in K) Soccer field 180 50 Athletic field 130 20 Gymnasium 240 85 Swimming pool 270 40 Tennis center 70 15 The community has a $140K construction budget. The selection must also comply with the following two criteria: (1) At least two of the proposed facilities must be selected; and (2) gymnasium and tennis center cannot be selected simultaneously. Fill in the blanks to complete the formulation for this 0-1 integer programming model that maximizes the expected usage. You should type the missing coefficient values. (Hint: If a variable should not appear in a constraint, then you should type 0 for its coefficient value.) Max Z = 180 xg+ 130 xa + 240 xg + Xp + st. 50 xs + 20 xa + Xg + Xp + 15 x4s 140 1 xg + 1 xg + 1 xg + 1 xXp + 1 x¢2 Xa+ Xg+ Xp+ Xj is binary for all i
Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter2: Introduction To Spreadsheet Modeling
Section: Chapter Questions
Problem 20P: Julie James is opening a lemonade stand. She believes the fixed cost per week of running the stand...
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Transcribed Image Text:A community council must decide which recreation facilities to construct in its community. Five new recreation facilities have been proposed – a soccer field (xs), an athletic field (Xa), a gymnasium (xg), a swimming pool (xp), a
tennis center (x;). The council wants to select facilities that will maximize the expected daily usage by the residents of the community, subject to budget and selection limitations. The expected daily usage and cost information for
each facility are given below:
Recreation Facility
Expected Usage (people/day)
Cost ($ in K)
Soccer field
180
50
Athletic field
130
20
Gymnasium
240
85
Swimming pool
270
40
Tennis center
70
15
The community has a $140K construction budget. The selection must also comply with the following two criteria: (1) At least two of the proposed facilities must be selected; and (2) gymnasium and tennis center cannot be selected
simultaneously.
Fill in the blanks to complete the formulation for this 0-1 integer programming model that maximizes the expected usage. You should type the missing coefficient values. (Hint: If a variable should not appear in a constraint, then you
should type 0 for its coefficient value.)
Max Z = 180 Xg + 130 xa + 240 xg +
0 xg*
Xp +
st.
50 xs + 20 xa +
Xg +
Xp + 15 x4s 140
1 xs + 1 xa + 1 xg + 1 xp + 1 x2
Xs+
Xa+
Xg+
Xp+
X; is binary for all i
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