"Mathematical Programming", "The Geometric Method"

Question 1

Simple Q&A

In the geometric representation of an LP, what does an inequality constraint correspond to on a graph?

Think about how an inequality divides the coordinate plane.

Answer 1

A half-plane that contains the eligible (feasible) solutions.

Question 2

Missing Word

The region where all constraints of a Linear Programme are satisfied simultaneously is called the _____ _____.

This is the set of possible solutions before considering the objective

Answer 2

feasible space (or feasible region)

Question 3

Simple Q&A

In a graphical LP solution, how do you find the optimal point for a minimization problem?

Think about moving the objective function line.

Answer 3

Move the objective function line parallel to itself in the direction that decreases its value. The last point of contact with the feasible region before it exits is the optimum.

Question 4

Definition

What does it mean if a Linear Programme is “Unbounded”?

Answer 4

The objective function can be improved (maximized or minimized) indefinitely without violating the constraints. The feasible region extends infinitely in the direction of improvement.

Question 5

Definition

What does it mean if a Linear Programme is “Infeasible”?

Answer 5

There is no solution that satisfies all constraints simultaneously. The constraints are mutually exclusive, so the feasible region is empty.

No decision variable values can meet all the requirements at once.

Question 6

Method

What is the “Corner Point” method for solving a Linear Programme graphically?

Answer 6

1. Identify all the corner points (vertices) of the feasible region
2. Calculate the value of the objective function at each corner point
3. Select the corner point that gives the best value (highest for maximization, lowest for minimization)