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Chapter 7: 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 that the solution to the problem must fulfill. Constraints are typically represented as linear inequalities or equations.

Step by step solution

01

Understanding a Constraint

A constraint, in a Linear Programming (LP) problem, is a condition that must be met, or a restriction that the solution to the LP problem must adhere to. In other words, constraints limit the feasible solutions in a LP problem. For instance, in a product mix problem, a company may have constraints related to the availability of resources like labor hours, machine hours, or raw materials.
02

Representation of Constraints

In a LP problem, constraints are typically represented as linear inequalities or equations. For instance, if we have a resource like labor hours, the constraint might be represented as \(2x + 3y \leq 40\), where \(x\) and \(y\) are variables representing different products, 2 and 3 are the labor hours required for each product and 40 is the total labor hours available. This constraint indicates that the combination of products made should not require more than the total labor hours available.

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Most popular questions from this chapter

What is a system of linear inequalities?

Will help you prepare for the material covered in the next section. In each exercise, graph the linear function. $$f(x)=-2$$

Determine whether each statement makes sense or does not make sense, and explain your reasoning. I graphed a nonlinear system that modeled the orbits of Earth and Mars, and the graphs indicated the system had a solution with a real ordered pair.

Find the length and width of a rectangle whose perimeter is 36 feet and whose area is 77 square feet.

Determine whether each statement makes sense or does not make sense, and explain your reasoning. Every linear system has infinitely many ordered-pair solutions.
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