# Question Video: Identifying the Correct Terminology for the Linear Inequalities of a Linear Programming Problem Mathematics • 9th Grade

Complete the following: The linear inequalities or restrictions on the variables of a linear programming problem are called ＿. [A] optimal values [B] maximum values [C] minimum values [D] objective functions [E] constraints

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### Video Transcript

Complete the following: The linear inequalities or restrictions on the variables of a linear programming problem are called what. Is it (A) optimal values, (B) maximum values, (C) minimum values, (D) objective functions, or (E) constraints?

Let’s begin by considering what each of the options mean in terms of a linear programming problem. We recall that linear programming is a technique used to find an optimal value of a linear objective function given a collection of linear constraints. This means that the optimal value or values are not the linear inequalities or restrictions. This optimal solution occurs at one of the vertices of the feasible region. We can therefore rule out option (A). Maximum and minimum values or solutions are types of optimal solution. So, we can also rule out options (B) and (C).

This leaves us with objective functions and constraints. An objective function is a linear function of the variables. As already mentioned, it is this that we are trying to find the optimal value of when solving a linear programming problem. This means that we can also rule out option (D). Option (E), however, is the correct answer. The restrictions placed on a linear programming problem are known as constraints.

We can therefore conclude that the linear inequalities or restrictions on the variables of a linear programming problem are called constraints. The correct answer is option (E).