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

question 27

Multiple Choice

Note: This problem requires the use of a linear programming application such as Solver or Analytic Solver.
The university administration would like to add some additional parking locations. To make everyone happy, they would like each building to be within a 5 minute walk of one set of new parking spaces (the spaces will be added in blocks of 10 parking spaces) . The university is considering six locations for the new parking spaces, but would like to minimize the overall cost of the project. In addition to the walking time requirement, the university would like to add at least 40 new parking spaces (at least 4 blocks of 10) . To help with the decision, the management science department formulated the following linear programming model:
Min 400x1 + 375x2 + 425x3 + 350x4 +410x5 + 500x6
s.t. x1 + x2 + x5 + x6 ? 1{Residence Hall A constraint}
X1 + x2 + x3 ? 1 {Residence Hall B constraint}
X4 + x5 + x6 ? 1 {Science building constraint}
X1 + x4 + x5 ? 1 {Music building constraint}
X2 + x3 + x4 ? 1 {Math building constraint}
X3 + x4 + x5 ? 1 {Business building constraint}
X2 + x5 + x6 ? 1 {Auditorium constraint}
X1 + x4 + x6 ? 1 {Arena constraint}
X1 + x2 + x3 + x4 + x5 + x6 ? 4 {Total locations constraint} xj={1, if location j is selected 0, otherwise x _ { j } = \left\{ \begin{array} { l } 1 , \text { if location } j \text { is selected } \\0 , \text { otherwise }\end{array} \right.
Set up the problem in Excel and find the optimal solution. Which locations are selected?

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Definitions:

Selling and Administrative Expenses

Costs associated with the selling of products and the management of the business.

Fixed Overhead

The total non-variable costs associated with operating a business, including rent, salaries, and insurance, that remain unchanged regardless of the level of production or sales.

Direct Labor

The wages and other forms of remuneration paid to employees who directly work on the products being manufactured, such as assembly line workers.

Property, Plant, and Equipment

Long-term tangible assets used in the operation of a business, such as buildings, machinery, and equipment.

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