Which of the following is NOT considered a type of linear programming problem?

Linear programming is a mathematical technique used for optimizing a linear objective function, subject to linear equality and inequality constraints. The question requires identifying a type of problem that does not fall under the umbrella of linear programming applications.

Resource-allocation problems, cost-benefit tradeoff problems, and transportation problems are all classic examples of linear programming scenarios, where they involve optimizing resources, costs, or logistics within set constraints. Each of these aligns with the fundamental principles of linear programming, which is about maximizing or minimizing a linear objective function while adhering to constraints.

Feasibility problems, on the other hand, are generally concerned with determining whether a set of constraints can be satisfied without necessarily focusing on optimizing a particular objective function. These problems ask questions about the existence of solutions to a set of linear inequalities, rather than trying to find the best solution according to some criterion. This distinction is significant, as feasibility problems do not align with the primary goals of linear programming, which includes optimization.

This clarifies why feasibility problems are not considered a type of linear programming problem. They do not involve the optimization aspect that characterizes the other types listed, making it the correct answer to the question.