Activity Overview

Consider this problem:

All profit-making businesses want to maximise their profits and minimise their losses. In order to achieve this, they obviously have to make decisions. 

This activity will look at one of the tools that is commonly used in business for decision making: linear programming.

Let’s look at an example problem.

A bakery makes two types of bread;  let’s calls them Bread A and Bread B. The dough for each bread is a mixture of wholemeal flour, spelt flour and strong white bread flour. The flours are in different proportions.

Bread A sells for twice as much as Bread B, and for each day in the bakery there is a fixed amount of wholemeal flour and white bread flour. The bakery would like to know how much of Bread A and Bread B to make in order to maximise their sales. 

How can linear programming help with this problem?

Linear programming and optimisation

Linear programming can help the bakery make a decision about how much of each product to produce to maximise its profit, while staying within the constraints of its resources and budget.  This is called optimisation: finding the best solution among a set of possible solutions.

A business can do this by using linear equations to represent the costs, revenues and constraints and then by finding the optimum solution that satisfies all of the constraints.

Linear programming has many applications in many fields  and is important in many real-world situations, such as in business, finance and engineering. It helps people make better decisions and use their resources more efficiently.  

Learning objectives

By the end of this activity, you will be able to:

• Assess the criteria and constraints in a decision-making process using linear optimisation.