Unlocking the Power of Decision Variables

What types of decision variables are necessary for this problem?

continuous, pure integer, integer and binary, pure binary

Final Answer:

The types of decision variables required in a mathematical problem depend on the context. For the given survey on books, the discrete variables are the number of books, while the continuous variables are the amounts of money involved.

When addressing a mathematical problem involving decision variables, it is crucial to understand the types of variables present. In the context of a survey examining the number of books students purchased and sold, and the corresponding amount paid and received, we can classify the variables accordingly. The discrete variables are the number of books purchased and the number of books sold, as they refer to countable quantities. Conversely, the continuous variables are the amount of money spent purchasing books and the amount of money received from selling them, since money can be measured on a continuous scale.

Decision variables can be of different types, including continuous, pure integer, integer and binary, pure binary, or a combination of continuous, integer, and binary. Continuous variables can take any value within a range, while integers are whole numbers, and binary variables are restricted to the values 0 or 1. The context of the problem will determine which types of variables are necessary. For example, if we were to optimize for profit from buying and selling books, we might use integers for the number of books and continuous variables for the costs and revenues.