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 strawberries and apples. Use the information below to write a report for Ian making recommendations as to how many hectares of each type he should grow.

Information:

• Strawberries require 33 hours of labour per hectare and apples require 77 hours of labour per hectare.
• Strawberries require 42 litres of fertiliser per hectare and apples require 49 litres of fertiliser per hectare.
• Ian has a maximum of 2541 hours of labour and 2058 litres of fertiliser.
• Ian must grow at least 6 hectares of apples and at least 7 hectares of strawberries.

Income predictions:

• For the current year, he expects to receive $1859 per hectare for his apples and $1809 per hectare for his strawberries.
• He is unsure of the future income from apples, but he thinks that next year will be approximately $2110.5 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: