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

Information:

• Chillies require 47 hours of labour per hectare and grapes require 188 hours of labour per hectare.
• Chillies require 27 litres of fertiliser per hectare and grapes require 12 litres of fertiliser per hectare.
• Ian has a maximum of 8836 hours of labour and 1620 litres of fertiliser.
• Ian must grow at least 9 hectares of grapes and at least 4 hectares of chillies.

Income predictions:

• For the current year, he expects to receive $955 per hectare for his grapes and $1524 per hectare for his chillies.
• He is unsure of the future income from grapes, but he thinks that next year will be approximately $6096 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: