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A Level Further Maths Decision 1 > Linear Programming > Flashcards

Flashcards in Linear Programming Deck (14)
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1

Decision variables

The letters that represent the thing that varies in the problem

2

Objective function

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

3

Constraints

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

4

Feasible solution

Values for the decision variables that satisfy each constraint

5

Feasible region

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

6

Optimal solution

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

7

Formulating a problem as a linear programming problem

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

8

What part of the graph do you shade?

The areas that fail to satisfy the inequality

9

Feasible region

The region of the graph that satisfies all the constraints

10

Objective line method

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

11

Rules of constraints

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

12

Vertex Testing Method

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

13

Vertex testing method table

(x,y) | max/min nx + my
--------|--------------------------
(x1,y1)| n(x1) + m(y1) = ...

14

Integer solutions method

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