Final answer:
Integer decision variables are necessary in situations where items cannot be divided, such as inventory management, project scheduling, and seating arrangements, because they represent discrete, indivisible units.
Step-by-step explanation:
Examples of Integer Decision Variables
Decision variables need to be integers in various contexts where quantifiable items cannot be divided into smaller parts. These are often known as discrete variables and are relevant in numerous applications.
Inventory Management: The number of items in stock, such as cars or pairs of shoes, are represented by integer decision variables because fractional items are not practical.
Project Scheduling: The number of projects or tasks assigned to employees. Each project or task is a whole entity, and you can't have part of a task or project, so integer variables are used.
Seating Arrangements: The number of seats in a venue. Seats are discrete units and cannot be fractioned, necessitating the use of integers.
These examples emphasize the need for decision variables to be discrete and quantitatively specific in order to facilitate effective decision making in respective applications.