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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 355x1 + 410x2 + 425x3+ 415x4 + 500x5 + 405x6 s.t. x1 + x2 + x5 + x6 2 1 (Residence Hall A constraint} 2 1 (Residence Hall B constraint} x1 x2 X3 x4 + x5 + x6 2 1(Science building constraint} 2 1 (Music building constraint} x4 2 1 (Math building constraint} x5 2 1 (Business building constraint} 2 1(Auditorium constraint} X1 X4 X5 x2 + X3 x3 + x4 x2 X5 X6 x6 z 1 (Arena constraint} x3 + x4 + x5 + x6 z 4 (Total locations constraint} 1, if location j is selected 0, otherwise X1 + X4 x1 + x2 a. What is the minimum the university can spend and still meet its goals? (Round your answer to the nearest whole number.) Minimum university goals

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 355x1 + 410x2 + 425x3+ 415x4 + 500x5 + 405x6 s.t. x1 + x2 + x5 + x6 2 1 (Residence Hall A constraint} 2 1 (Residence Hall B constraint} x1 x2 X3 x4 + x5 + x6 2 1(Science building constraint} 2 1 (Music building constraint} x4 2 1 (Math building constraint} x5 2 1 (Business building constraint} 2 1(Auditorium constraint} X1 X4 X5 x2 + X3 x3 + x4 x2 X5 X6 x6 z 1 (Arena constraint} x3 + x4 + x5 + x6 z 4 (Total locations constraint} 1, if location j is selected 0, otherwise X1 + X4 x1 + x2 a. What is the minimum the university can spend and still meet its goals? (Round your answer to the nearest whole number.) Minimum university goals

Practical Management Science
Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter5: Network Models
Section5.3: Assignment Models
Problem 11P
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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 355x1 + 410x2 + 425x3+ 415x4 + 500x5 + 405x6 s.t. x1 + x2 + x5 + x6 2 1 (Residence Hall A constraint) x1 + x2 + x3 2 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 + x5 2 1 (Business building constraint} x2 + x5 + x6 2 1(Auditorium constraint} X1 + x4 + x6 2 1(Arena constraint} X1 + x2 + x3 + x4 + x5 + x6 2 4 {Total locations constraint) 1, if location j is selected 0, otherwise Xj = a. What is the minimum the university can spend and still meet its goals? (Round your answer to the nearest whole number.) Minimum university goals
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 355x1 + 410x2 + 425x3+ 415x4 + 500x5 + 405x6 s.t. x1 + x2 + x5 + x6 2 1 (Residence Hall A constraint) x1 + x2 + x3 2 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 + x5 2 1 (Business building constraint} x2 + x5 + x6 2 1(Auditorium constraint} X1 + x4 + x6 2 1(Arena constraint} X1 + x2 + x3 + x4 + x5 + x6 2 4 {Total locations constraint) 1, if location j is selected 0, otherwise Xj = a. What is the minimum the university can spend and still meet its goals? (Round your answer to the nearest whole number.) Minimum university goals
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