Linear Programming

Question 1

Decision variables

Answer 1

The letters that represent the thing that varies in the problem

Question 2

Objective function

Answer 2

How you get to what you are trying to minimise and maximise and whether it is a minimise or maximise

Question 3

Constraints

Answer 3

The things that present you using an infinite amount of each variable. Each will give rise to one inequality

Question 4

Feasible solution

Answer 4

Values for the decision variables that satisfy each constraint

Question 5

Feasible region

Answer 5

The region that contains all the feasible solutions in a graphical problem

Question 6

Optimal solution

Answer 6

The feasible solution that meets the objective - there may be multiple optimal solutions

Question 7

Formulating a problem as a linear programming problem

Answer 7

1) Define the decision variables (e.g. x = …)
2) State the objective (minimise/maximise variable = ax + by …)
3) Write the constraints as inequalities (x, y >= 0, must be written in terms of integers and simplified

Question 8

What part of the graph do you shade?

Answer 8

The areas that fail to satisfy the inequality

Question 9

Feasible region

Answer 9

The region of the graph that satisfies all the constraints

Question 10

Objective line method

Answer 10

Choose a value for the objective function and plot that
Draw the line parallel to it which is highest/lowest in the feasible region
Substitute the values
If it is not easy to draw the line solve as simultaneous equations

Question 11

Rules of constraints

Answer 11

x,y >= 0
Must be in terms of integers
Must be simplified

Question 12

Vertex Testing Method

Answer 12

1) Find the coordinates of the vertices of the feasible region, including (0,0) and vertices made with the axes
2) Evaluate the objective function at each of these points in a table
3) Select the vertex that gives an optimal value

Question 13

Vertex testing method table

Answer 13

(x,y) | max/min nx + my
——–|————————–
(x1,y1)| n(x1) + m(y1) = …

Question 14

Integer solutions method

Answer 14

1) Find the optimal vertex
2) Find all the combinations of x and y rounded up/down to the next integer
3) Using the inequalities that make the vertex, substitute the points into each and see if it works in a table, if it doesn’t don’t check again
4) See which one makes the best solution if multiple points remain