The university administration would like to add some additional parking locations. To make everyone happy, they would like each building to be within a 5 minute walk of one set of new parking spaces (the spaces will be added in blocks of 10 parking spaces). The university is considering six locations for the new parking spaces, but would like to minimize the overall cost of the project. In addition to the walking time requirement, the university would like to add at least 40 new parking spaces (at least 4 blocks of 10). To help with the decision, the management science department formulated the following linear programming model: Min 400x1 + 375x2 + 425x3 + 350x4 +410x5 + 500x6 s.t. x1 + x2 + x5 + X6 ≥ 1 (Residence Hall A constraint) x1 + x2 + x3 ≥ 1 (Residence Hall B constraint) X4 X5 X6 2 1 (Science building constraint) X1 + X4 X5 2 1 (Music building constraint) x2 + x3 + x4 2 1 (Math building constraint) x3 + x4 x2 + x5 X1 + X4+ X6 ≥ 1 (Arena constraint) x5 2 x6 2 1 (Auditorium constraint) 1 (Business building constraint) x1 + x2 + x3 + x4 + X5 + X6 ≥ 4 (Total locations constraint) 1, if location j is selected xj = {0, otherwise Which of the locations is within 5 minutes of the science, music, math, and business buildings? Multiple Choice Location 4 Location 2 Location 5 Location 6
The university administration would like to add some additional parking locations. To make everyone happy, they would like each building to be within a 5 minute walk of one set of new parking spaces (the spaces will be added in blocks of 10 parking spaces). The university is considering six locations for the new parking spaces, but would like to minimize the overall cost of the project. In addition to the walking time requirement, the university would like to add at least 40 new parking spaces (at least 4 blocks of 10). To help with the decision, the management science department formulated the following linear programming model: Min 400x1 + 375x2 + 425x3 + 350x4 +410x5 + 500x6 s.t. x1 + x2 + x5 + X6 ≥ 1 (Residence Hall A constraint) x1 + x2 + x3 ≥ 1 (Residence Hall B constraint) X4 X5 X6 2 1 (Science building constraint) X1 + X4 X5 2 1 (Music building constraint) x2 + x3 + x4 2 1 (Math building constraint) x3 + x4 x2 + x5 X1 + X4+ X6 ≥ 1 (Arena constraint) x5 2 x6 2 1 (Auditorium constraint) 1 (Business building constraint) x1 + x2 + x3 + x4 + X5 + X6 ≥ 4 (Total locations constraint) 1, if location j is selected xj = {0, otherwise Which of the locations is within 5 minutes of the science, music, math, and business buildings? Multiple Choice Location 4 Location 2 Location 5 Location 6
Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter2: Introduction To Spreadsheet Modeling
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Transcribed Image Text:The university administration would like to add some additional parking locations. To make everyone happy, they would like each building to be within a 5 minute walk of one set of new parking spaces (the spaces will
be added in blocks of 10 parking spaces). The university is considering six locations for the new parking spaces, but would like to minimize the overall cost of the project. In addition to the walking time requirement, the
university would like to add at least 40 new parking spaces (at least 4 blocks of 10). To help with the decision, the management science department formulated the following linear programming model:
Min 400x1 + 375x2 + 425x3 + 350x4 +410x5 + 500x6
s.t. X1 + X2 + X5 + X6 ≥ 1 {Residence Hall A constraint}
X1 + x2 + x3 ≥ 1 {Residence Hall B constraint}
X4 X5 X6 ≥ 1 {Science building constraint}
x1 + x4 + X5 ≥ 1 {Music building constraint}
x2 + x3 + x4 ≥ 1 {Math building constraint}
x3 + x4 + X5 ≥
1 (Business building constraint}
x2 + x5 + X6 ≥
X1 + X4+ X6 ≥
Xj =
x1 + x2 + x3 + x4 + X5 + X6 ≥ 4 {Total locations constraint}
if location j is selected
1 {Auditorium constraint}
1 (Arena constraint}
1,
{1, if location
Multiple Choice
Which of the locations is within 5 minutes of the science, music, math, and business buildings?
O
Location 4
Location 2
Location 5
Location 6
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