Decision 6: Linear Programming

Question 1

How is a linear programming problem set up? (3)

Answer 1

Define the decision variables
State the objective and objective function
Write the constraints as inequalities

Question 2

What is the feasible region?

Answer 2

The region of a graph that satisfies all the constraints of a linear programming problem

Question 3

How do you find the optimal solution using the vertex method? (2)

Answer 3

Find the coordinates of each intersection between inequalities
Evaluate the objective function at each point

Question 4

How do you find the optimal solution using the ruler method? (2)

Answer 4

Draw a line on the graph of objective gradient and set your ruler to that gradient
Move the ruler up the page and find either the last point covered (maximises) or the first point covered (minimises)

Question 5

How do you find integer solutions?

Answer 5

Consider points with integer coordinates near the optimal vertex