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 375x1 + 380x2 + 415x3+ 485x4 + 460x5 + 480x6 s.t. x1 + x2 + xs + 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 jis selected 0, otherwise Ij = a. What is the minimum the university can spend and still meet its goals? (Round your answer to the nearest whole number.)
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 375x1 + 380x2 + 415x3+ 485x4 + 460x5 + 480x6 s.t. x1 + x2 + xs + 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 jis selected 0, otherwise Ij = a. What is the minimum the university can spend and still meet its goals? (Round your answer to the nearest whole number.)
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: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 375x1 + 380x2 + 415x3+ 485x4 + 460x5 + 480x6
s.t. x1 + x2 + xs + x6 2 1 (Residence Hall A constraint)
x1 + x2 + x3 2 1 (Residence Hall B constraint)
2 1 (Science building constraint)
x1 + x4 + x5 2 1(Music building constraint)
x2 + x3 + X4 2 1(Math building constraint)
x3 + X4 + xs 2 1(Business building constraint)
x2 + xs + x6 2 1 (Auditorium constraint)
x1 + X4 + X6 2 1(Arena constraint)
X1 + x2 + x3 + x4 + x5 + x6 2 4 (Total locations constraint)
S1, if locationjis selected
10, otherwise
X4 + X5 + X
%3D
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
b. Which of the locations will be selected?
Location 1 wil
Location 2 wil
Location 3 will
Location 4 will
Location 5 will
Location 6 will
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