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Chapter 5: Problem 26

What is a constraint in a linear programming problem? How is a constraint represented?

Short Answer

Expert verified
In a linear programming problem, a constraint is a condition or limit expressed in an inequality or equation. In a graphical representation, each constraint is often represented as a line dividing the feasible region in the coordinate plane.

Step by step solution

01

Definition of a Constraint

In a linear programming problem, a constraint is a condition that must be met. These conditions are given in the form of inequalities or equations, and they limit the possible solutions of the problem. The constraints represent restrictions or limitations on the possible solutions to the problem.
02

Representation of a Constraint

In a linear programming problem, each constraint is often represented graphically as a line (in case the problem is a two-variable problem) in a coordinate plane. Each point in the region that satisfies all the inequality constraints is a feasible solution to the problem.
03

Example of a Constraint

For example, if you have a simple linear programming problem with two variables, x and y, and two constraints: x + y <= 5 and x >= 1, these constraints will be represented as lines dividing the feasible region (possible values of x and y) in the coordinate plane.

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Most popular questions from this chapter

In Exercises \(5-18\), solve each system by the substitution method. $$ \begin{aligned} &2 x-3 y=-13\\\ &y=2 x+7 \end{aligned} $$

In Exercises \(5-18\), solve each system by the substitution method. $$ \begin{array}{l} x=4 y-2 \\ x=6 y+8 \end{array} $$

In Exercises \(31-42,\) solve by the method of your choice. Identify systems with no solution and systems with infinitely many solutions, using set notation to express their solution sets. \(x=9-2 y\) \(x+2 y=13\)

In Exercises \(5-18\), solve each system by the substitution method. $$ \begin{array}{l} 2 x+5 y=1 \\ -x+6 y=8 \end{array} $$

In Exercises \(5-18\), solve each system by the substitution method. $$ \begin{aligned} &x+y=6\\\ &y=2 x \end{aligned} $$
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