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 + xg 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 1 {Building H constraint} x1 + X4 + xg 2 1(Building I constraint) x1 + x2 + x7 1 (Building J constraint} 1, if crew j is selected 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?

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 + xg 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 1 {Building H constraint} x1 + X4 + xg 2 1(Building I constraint) x1 + x2 + x7 1 (Building J constraint} 1, if crew j is selected 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?

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter6: Optimization Models With Integer Variables

Section6.5: Set-covering And Location-assignment Models

Problem 29P

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