Question

In a linear programming problem, the linear function which has to be maximized or minimized is called

• A. a feasible function
• B. an objective function
• C. an optimal function
• D. a constraint

Hint:

In every Linear Programming problem, the equation you want to maximize or minimize is always called the \textbf{Objective Function}.

Answer 1

The Correct Option is B

In linear programming, the given question asks about the term used to describe the function that needs to be maximized or minimized. To address this, let's explore the fundamental concepts of linear programming, which is a mathematical technique used for optimizing outputs under a given set of constraints.

1. In linear programming, each problem involves:
   • An objective function: This is the linear function that represents the goal of the operation, such as maximizing profit or minimizing cost. In other words, it is the function being optimized.
   • Constraints: These are the linear inequalities or equations that define the feasible region or the limits within which the objective function must be optimized.
2. We are asked to identify the term for the function that must be maximized or minimized, which aligns perfectly with the description of the objective function.
3. Let's analyze each option:
   • a feasible function: This term is not conventionally used in linear programming. It might refer informally to a function that meets certain criteria, but it is not correct in this context.
   • an objective function: As described, this is the correct term for the function to be optimized in linear programming.
   • an optimal function: This term is not standard in linear programming, as "optimal" generally describes the state of having the best solution, not the function itself.
   • a constraint: Constraints limit the values that the decision variables can take and define the feasible region but are not optimized themselves.

Therefore, the correct answer is "an objective function". This term accurately describes the function that needs to be either maximized or minimized in a linear programming problem.