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 270x₁ + 290x2 + 250x3+ 270x4 + 230x5 + 180x6 + 180x7+280x8 s.t. x1 + x2 + x5 + x7 2 1 {Building A constraint} x1 + x2 + x3 2 1 (Building B constraint} 1 [Building C constraint} X6 + x8 x1 + x4 + x7 2 1 (Building D constraint} x2 + x7 ≥ 1 {Building E constraint} x3 + x8 2 1 [Building F constraint} x2 + x5 + x7 2 1 (Building G constraint} x1 + x4 + x6 ≥ 1 (Building H constraint} x1 + x4 + x8 ≥ 1 (Building I constraint} x1 + x2 + x7 2 1 (Building J constraint} J1, if crew jis selected xj = 10, 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
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 270x₁ + 290x2 + 250x3+ 270x4 + 230x5 + 180x6 + 180x7+280x8 s.t. x1 + x2 + x5 + x7 2 1 {Building A constraint} x1 + x2 + x3 2 1 (Building B constraint} 1 [Building C constraint} X6 + x8 x1 + x4 + x7 2 1 (Building D constraint} x2 + x7 ≥ 1 {Building E constraint} x3 + x8 2 1 [Building F constraint} x2 + x5 + x7 2 1 (Building G constraint} x1 + x4 + x6 ≥ 1 (Building H constraint} x1 + x4 + x8 ≥ 1 (Building I constraint} x1 + x2 + x7 2 1 (Building J constraint} J1, if crew jis selected xj = 10, 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
Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter12: Queueing Models
Section: Chapter Questions
Problem 59P
Related questions
Question
![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](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fca4639e1-ad6a-4442-8c8c-fb1994ba5fd4%2F0b9cbbd0-fbf8-4575-927a-604cb57fe38d%2F0yz6zr_processed.png&w=3840&q=75)
Transcribed Image Text: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 270x1 + 290x2 + 250x3+ 270x4 + 230x5 + 180×6 + 180×7 + 280x8
S.t. x₁ + x2 + x5 + x7 ≥ 1 {Building A constraint}
X1 + x2 + x3 ≥ 1 {Building B constraint}
X6 + x8 ≥ 1 {Building C constraint}
X1 + x4 + x7 ≥ 1 {Building D constraint}
x2 + x7 ≥ 1 {Building E constraint}
x3 + x8 ≥ 1 {Building F constraint}
x2 + x5 + x7 ≥ 1 (Building G constraint}
x1 + x4 + x6 ≥ 1 {Building H constraint}
X1 + x4 + x8 ≥ 1 {Building I constraint}
x1 + x2 + x7 ≥ 1 {Building J constraint}
xj
=
ſ 1, if crew jis selected
10, 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](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fca4639e1-ad6a-4442-8c8c-fb1994ba5fd4%2F0b9cbbd0-fbf8-4575-927a-604cb57fe38d%2Fhqxcv8o_processed.png&w=3840&q=75)
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 270x1 + 290x2 + 250x3+ 270x4 + 230x5 + 180×6 + 180×7 + 280x8
S.t. x₁ + x2 + x5 + x7 ≥ 1 {Building A constraint}
X1 + x2 + x3 ≥ 1 {Building B constraint}
X6 + x8 ≥ 1 {Building C constraint}
X1 + x4 + x7 ≥ 1 {Building D constraint}
x2 + x7 ≥ 1 {Building E constraint}
x3 + x8 ≥ 1 {Building F constraint}
x2 + x5 + x7 ≥ 1 (Building G constraint}
x1 + x4 + x6 ≥ 1 {Building H constraint}
X1 + x4 + x8 ≥ 1 {Building I constraint}
x1 + x2 + x7 ≥ 1 {Building J constraint}
xj
=
ſ 1, if crew jis selected
10, 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
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