3.2 Question Generator - TJ's Farm
Introduction:
This activity requires you to use linear programming to model the constraints TJ 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:
TJ owns a farm and grows avocados and chillies. Use the information below to write a report for TJ making recommendations as to how many hectares of each type he should grow.

Information:

• Avocados require 2 hours of labour per hectare and chillies require 30 hours of labour per hectare.
• Avocados require 34 litres of fertiliser per hectare and chillies require 2 litres of fertiliser per hectare.
• TJ has a maximum of 1620 hours of labour and 1632 litres of fertiliser.
• TJ must grow at least 17 hectares of chillies and at least 15 hectares of avocados.

Income predictions:

• For the current year, he expects to receive $607 per hectare for his chillies and $1162 per hectare for his avocados.
• He is unsure of the future income from chillies, but he thinks that next year will be approximately $17430 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: