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The university is scheduling cleaning crews for its ten buildings. Each crew has a different cost and is qualified to clean only certain buildings. There are eight possible crews to choose from in this case. The goal is to minimize costs while making sure that each building is cleaned. The management science department formulated the following linear programming model to help with the selection process. Min 210x1 + 200x2 + 300x3+ 250x4 + 260x5 + 240x6 + 260x7 + 290xg s.t. x1 + x2 + x5 + x7 2 1(Building A constraint} x1 + x2 + x3 2 1(Building B constraint} X6 + x8 2 1{Building C constraint) X1 + X4 + x7 2 1{Building D constraint) x2 + x7 2 1{Building E constraint} x3 + xg 2 1{Building F constraint} x2 + x5 + x7 2 1{Building G constraint) X1 + X4 + x6 2 1{Building H constraint) X1 + X4 + xg 2 1{Building I constraint) X1 + x2 + x7 2 1(Building J constraint) S1, if crew jis selected 0, otherwise *j = Set up the problem in Excel and find the optimal solution. a. What is the cost of the optimal crew assignment? Cost of optimal crew assignment b. Which crews are assigned to work? Crew 1 will Crew 2 will Crew 3 will Crew 4 will Crew 5 will Crew 6 will Crew 7 will Crew 8 will

The university is scheduling cleaning crews for its ten buildings. Each crew has a different cost and is qualified to clean only certain buildings. There are eight possible crews to choose from in this case. The goal is to minimize costs while making sure that each building is cleaned. The management science department formulated the following linear programming model to help with the selection process. Min 210x1 + 200x2 + 300x3+ 250x4 + 260x5 + 240x6 + 260x7 + 290xg s.t. x1 + x2 + x5 + x7 2 1(Building A constraint} x1 + x2 + x3 2 1(Building B constraint} X6 + x8 2 1{Building C constraint) X1 + X4 + x7 2 1{Building D constraint) x2 + x7 2 1{Building E constraint} x3 + xg 2 1{Building F constraint} x2 + x5 + x7 2 1{Building G constraint) X1 + X4 + x6 2 1{Building H constraint) X1 + X4 + xg 2 1{Building I constraint) X1 + x2 + x7 2 1(Building J constraint) S1, if crew jis selected 0, otherwise *j = Set up the problem in Excel and find the optimal solution. a. What is the cost of the optimal crew assignment? Cost of optimal crew assignment b. Which crews are assigned to work? Crew 1 will Crew 2 will Crew 3 will Crew 4 will Crew 5 will Crew 6 will Crew 7 will Crew 8 will

Practical Management Science
Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter3: Introduction To Optimization Modeling
Section: Chapter Questions
Problem 52P
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The university is scheduling cleaning crews for its ten buildings. Each crew has a different cost and is qualified to clean only certain buildings. There are eight possible crews to choose from in this case. The goal is to minimize costs while making sure that each building is cleaned. The management science department formulated the following linear programming model to help with the selection process. Min 210x1 + 200x2 + 300x3+ 250x4 + 260x5 + 240x6 + 260x7 + 290xg s.t. x1 + x2 + x5 + x7 2 1{Building A constraint} x1 + x2 + x3 2 1{Building B constraint} 2 1 (Building C constraint} x1 + X4 + x7 2 1{Building D constraint} x2 + x7 2 1{Building E constraint} 2 1{Building F constraint} x2 + x5 + x7 2 1{Building G constraint} x1 + X4 + X6 2 1{Building H constraint} X1 + X4 + xg 2 1{Building I constraint) X1 + x2 + x7 2 1{Building J constraint) X6 + X8 X3 + X8 [1, if crew j is selected Tj 0, otherwise Set up the problem in Excel and find the optimal solution. a. What is the cost of the optimal crew assignment? Cost of optimal crew assignment b. Which crews are assigned to work? Crew 1 will Crew 2 will Crew 3 will Crew 4 will Crew 5 will Crew 6 will Crew 7 will Crew 8 will
Transcribed Image Text:The university is scheduling cleaning crews for its ten buildings. Each crew has a different cost and is qualified to clean only certain buildings. There are eight possible crews to choose from in this case. The goal is to minimize costs while making sure that each building is cleaned. The management science department formulated the following linear programming model to help with the selection process. Min 210x1 + 200x2 + 300x3+ 250x4 + 260x5 + 240x6 + 260x7 + 290xg s.t. x1 + x2 + x5 + x7 2 1{Building A constraint} x1 + x2 + x3 2 1{Building B constraint} 2 1 (Building C constraint} x1 + X4 + x7 2 1{Building D constraint} x2 + x7 2 1{Building E constraint} 2 1{Building F constraint} x2 + x5 + x7 2 1{Building G constraint} x1 + X4 + X6 2 1{Building H constraint} X1 + X4 + xg 2 1{Building I constraint) X1 + x2 + x7 2 1{Building J constraint) X6 + X8 X3 + X8 [1, if crew j is selected Tj 0, otherwise Set up the problem in Excel and find the optimal solution. a. What is the cost of the optimal crew assignment? Cost of optimal crew assignment b. Which crews are assigned to work? Crew 1 will Crew 2 will Crew 3 will Crew 4 will Crew 5 will Crew 6 will Crew 7 will Crew 8 will
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