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Note: This problem requires the use of a linear programming application such as Solver or Analytic Solver.
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 200x1 + 250x2 + 225x3 + 190x4 +215x5 + 245x6 + 235x7 + 220x8
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 + x6 + x8 ? 1 {Building I constraint}
X1 + x2 + x7 ? 1 {Building J constraint}
Set up the problem in Excel and find the optimal solution. Which crews are selected?
Macy's
An American department store chain known for its diverse range of products, including clothing, accessories, home furnishings, and more.
Kohl's
An American department store retail chain, offering a wide selection of clothing, footwear, bedding, furniture, jewelry, beauty products, and housewares.
Conventional Supermarkets
Traditional brick-and-mortar grocery stores that offer a wide range of food and household products, often including a bakery, dairy, meat, and produce sections.
Competitive Reality
The actual market conditions in which businesses compete for customers, including the level of competition, market share distribution, and current consumer preferences.
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