Question

after some special presentations, the employees of the av center have to move overhead projectors back to classrooms. the table below indicates the buildings where the projectors are now (the sources), where they need to go (the destinations), and a measure of the distance between sites. if you were going to write this as a linear programming model, how many decision variables would there be, and how many constraints would there be?

Answer 1

To write a linear programming model for distributing overhead projectors, one needs the number of decision variables equal to the product of sources and destinations, and constraints equal to the sum of the number of sources and destinations, plus additional ones based on specific problem details like distances.

Step-by-step explanation:

The student's question is about setting up a linear programming model for distributing overhead projectors to various classrooms, which involves decision variables and constraints.

Each projector movement from a source to a destination represents a decision variable; thus, the number of decision variables would be the product of the number of sources and the number of destinations.

Constraints could include the limit on the number of projectors each destination needs, the number of projectors available at each source, and possibly the distance limitations if a maximum transportation distance is to be considered.

To determine the exact number of these variables and constraints, more specific details about the number of projectors, locations, and their requirements would be needed. In general, if there are m sources and n destinations, there would be m x n decision variables.

As for constraints, there would typically be m supply constraints (one for each source) and n demand constraints (one for each destination), and possibly additional constraints depending on the specific details of the problem, such as distance or transportation cost considerations.