Linear Programming Concepts and Constraints

This tutorial covers the calculation of slack and surplus variables, identification of binding constraints, and writing a linear programming (LP) model in standard form. It explains the graphical representation of an LP model, the concept of optimal solutions, and how to determine slack and surplus values. The tutorial also demonstrates converting inequalities to equalities by introducing slack and surplus variables, and provides an example to illustrate these concepts.

What are the main topics covered in this tutorial?

• Slack and surplus variables, binding constraints, and standard form

• Differential equations

• Graph theory and algorithms

• Probability and statistics

Where does the optimal solution occur in the LP model graph?

• At the origin

• At the intersection of the first two constraints

• At the midpoint of the graph

• At the intersection of all constraints

What is a binding constraint?

• A constraint that intersects at the optimal solution point

• A constraint that is not used at all

• A constraint that is always greater than zero

• A constraint that is irrelevant to the solution

What does a slack value of zero indicate?

• The resource is fully utilized

• The resource is underutilized

• The resource is overutilized

• The resource is irrelevant

In which type of constraint does the term 'slack' apply?

• Greater than or equal to constraints

• Less than or equal to constraints

• Equal constraints

• Non-linear constraints

What happens to the slack variable in a less than or equal to constraint when it is binding?

• It becomes zero

• It becomes positive

• It becomes negative

• It becomes irrelevant

What is the result of plugging the optimal solution into a non-binding constraint?

• The left side is less than the right side

• The left side equals the right side

• The constraint becomes irrelevant

• The left side is greater than the right side

What is the result of plugging the optimal solution into a binding constraint?

• The left side equals the right side

• The left side is less than the right side

• The left side is greater than the right side

• The constraint becomes irrelevant

What does a surplus value indicate?

• The amount by which we fall short of the minimum requirement

• The amount by which we exceed the minimum requirement

• The amount of unused resource

• The amount of overutilized resource

In which type of constraint does the term 'surplus' apply?

• Less than or equal to constraints

• Greater than or equal to constraints

• Non-linear constraints

• Equal constraints