To solve linear programming problems, we start by writing out our inequalities on a graph with an x-axis and a y-axis. This becomes particularly valuable when we have inequalities in two variables.

Exercise

Let’s start with exercise 17 from pages 197 and 198 of the extended textbook

The answers are below:

Linear Programming

There are effectively three steps to follow in a linear programming question:

1. Identify the lines that need to be drawn based on the information in the question (i.e. treat the inequalities like equations to start off with);
2. Draw little arrows on the lines to indicate which side of them is represented by the inequality;
3. Shade in the region which satisfies all of the lines that have been drawn on the graph.

Exercise

Now let’s complete exercise 18 from pages 200 to 202 of the extended textbook:

The answers are below: