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 270 x1 + 230x2 + 240x3+ 220x4 + 190x5 + 270x6 + 230x7 + 220x8 st. 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= {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? 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
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 270 x1 + 230x2 + 240x3+ 220x4 + 190x5 + 270x6 + 230x7 + 220x8
st. 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= {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?
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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