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

Information:

• Carrots require 6 hours of labour per hectare and oranges require 27 hours of labour per hectare.
• Carrots require 45 litres of fertiliser per hectare and oranges require 3 litres of fertiliser per hectare.
• Shivneel has a maximum of 5022 hours of labour and 1755 litres of fertiliser.
• Shivneel must grow at least 15 hectares of oranges and at least 18 hectares of carrots.

Income predictions:

• For the current year, he expects to receive $535 per hectare for his oranges and $648 per hectare for his carrots.
• He is unsure of the future income from oranges, but he thinks that next year will be approximately $2916 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: