3.2 Question Generator - Bradley's Farm
Introduction:
This activity requires you to use linear programming to model the constraints Bradley has for his farm and to make recommendations so that he can maximise his income in the current year and in future years. You will present your findings as a written report, supported by graphs, equations and relevant calculations.
The quality of your reasoning and how well you link this to the context will determine the overall grade.

Task:
Bradley owns a farm and grows potatoes and leeks. Use the information below to write a report for Bradley making recommendations as to how many hectares of each type he should grow.

Information:

• Potatoes require 2 hours of labour per hectare and leeks require 4 hours of labour per hectare.
• Potatoes require 8 litres of fertiliser per hectare and leeks require 2 litres of fertiliser per hectare.
• Bradley has a maximum of 224 hours of labour and 336 litres of fertiliser.
• Bradley must grow at least 20 hectares of leeks and at least 14 hectares of potatoes.

Income predictions:

• For the current year, he expects to receive $649 per hectare for his leeks and $773 per hectare for his potatoes.
• He is unsure of the future income from leeks, but he thinks that next year will be approximately $193.25 per hectare.

As you write your report take care to clearly communicate your findings using appropriate mathematical statements. Include graphs, equations, and relevant calculations.

Answer: