Note: This Problem Requires the Use of a Linear Programming $$x _ { j } = \left\{ \begin{array} { l } 1 , \text { if crew } j \text { is selected } \\0 , \text { otherwise }\end{array} \right.$$

question 7

Multiple Choice

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} $$x _ { j } = \left\{ \begin{array} { l } 1 , \text { if crew } j \text { is selected } \\0 , \text { otherwise }\end{array} \right.$$
Set up the problem in Excel and find the optimal solution. What is the cost of the optimal set of locations?

• A) 255
• B) 355
• C) 455
• D) 555
• E) 655

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Definitions:

Imports

Goods or services brought into one country from another for the purpose of trade or sale.

Cournot Duopolists

A market structure in which two companies assume the other's output to be constant when determining their optimal production levels.

Total Costs

The total of all expenses involved in creating goods or services, encompassing both constant and fluctuating costs.

Daily Profit

The net financial gain or loss a business experiences on a daily basis.