The University Is Scheduling Cleaning Crews for Its Ten Buildings $$x _ { j } = \left\{ \begin{array} { l } 1 , \text { if crew } j \text { is selected } \\0 , \text { otherwise }\end{array} \right.$$

question 48

Multiple Choice

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} $$x _ { j } = \left\{ \begin{array} { l } 1 , \text { if crew } j \text { is selected } \\0 , \text { otherwise }\end{array} \right.$$
Which of the constraints is a set covering constraint?

• A) Building A constraint
• B) Building C constraint
• C) Building F constraint
• D) All of the choices are correct.
• E) None of the choices is correct.

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Definitions:

Direct Materials Purchases Variance

The difference between the actual costs of direct materials purchased and the expected (or standard) costs, impacting the budget and potentially financial results.

Variable Overhead Efficiency Variance

A measure used in management accounting to assess the efficiency of variable production overhead based on the actual time taken to produce goods versus the expected time.

Standard Direct Labor-Hours

Standard direct labor-hours refer to the estimated hours of direct labor work required to produce one unit of a product or service, used for budgeting and variance analysis.

Variable Overhead Rate Variance

The difference between the actual variable overhead incurred and the standard cost assigned to those overheads, indicating efficiency in managing variable costs.