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

Information:

• Carrots require 38 hours of labour per hectare and coconuts require 133 hours of labour per hectare.
• Carrots require 6 litres of fertiliser per hectare and coconuts require 4 litres of fertiliser per hectare.
• Layne has a maximum of 5054 hours of labour and 288 litres of fertiliser.
• Layne must grow at least 6 hectares of coconuts and at least 14 hectares of carrots.

Income predictions:

• For the current year, he expects to receive $283 per hectare for his coconuts and $1185 per hectare for his carrots.
• He is unsure of the future income from coconuts, but he thinks that next year will be approximately $790 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: