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) = ...

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