1. D1: Linear Programming

2. D1: Linear Programming
Linear programming is another part of D1 that is useful in business. The skills you will learn can be applied to maximise profits or minimise costs.
As the image in the corner indicates, it will involve being able to draw inequalities on graphs.
Before you can begin working through linear programming problems, there are a few definitions to learn.

3. D1: Linear Programming
Firstly, the decision variables of a problem are the numbers of each of the things that can be varied. These decision variables will be represented by letters.
Say, for example, that you own a business that manufactures two kinds of chair, x or y. The decision variables will be the number of these chairs that can be made.
D1 linear programming problems always have two decision variables so that things can be represented on a set of axes.

4. D1: Linear Programming
The objective function is an equation to show the aim of the problem, which is either to maximise profit or minimise costs.
The objective function uses the decision variables. Profit-based objective functions usually start with “ Maximise P = ”.
Cost-based objective functions start with “Minimise C = ”.
There are also constraints in a linear programming problem. These occur because there are limits to the amount of resources that can be used or purchased. Each new constraint means a new inequality to influence the problem.

5. D1: Linear Programming
A set of values for the decision variables that satisfy all the constraints is a feasible solution.
If the problem has been represented graphically, there should be an area that has been left clear once all the inequalities have been plotted. This is called the feasible region and it contains all the feasible solutions.
The optimal solution is the feasible solution that meets the objective best (i.e. maximises profits or minimises costs). There can be more than one optimal solution. In most cases the optimal solution will need to be in whole numbers.

6. D1: Linear Programming
Linear programming problems usually contain a lot more text than other D1 problems. One of your first tasks may be turning that text into a set of inequalities.
The linear programming process involves:
Defining the decision variables [usually done for you]
Stating the objective function
Writing the constraints as inequalities
Representing these inequalities graphically
Identifying the optimal solution in the feasible region