Final answer:
The key categories of linear programming problems include cost-benefit-trade-off problems and resource-allocation problems, with linear programming used to achieve optimal outcomes in mathematical models subject to constraints.
Step-by-step explanation:
The key categories of linear programming problems are B. cost-benefit-trade-off problems and D. resource-allocation problems. Options A. advertising problems and C. mixed problems are not typically characterized as main categories under linear programming.
Linear programming is a mathematical method for determining a way to achieve the best outcome in a given mathematical model. This model usually comes in the form of optimizing a particular linear function, subject to a set of linear inequalities, known as constraints. The cost-benefit-trade-off problems involve finding a balance between different costs and benefits to reach an optimal point.
On the other hand, the resource-allocation problems focus on distributing limited resources in an efficient way. Examples include planning production levels to maximize profit or minimize costs while meeting customer demand, and scheduling workers and machines in a factory to optimize productivity.
By understanding different types of problems handled by linear programming, such as cost-benefit trade-offs and resource allocation, one can effectively apply this tool to various real-world optimization problems.