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

Information:

• Rock melons require 7 hours of labour per hectare and apples require 28 hours of labour per hectare.
• Rock melons require 4 litres of fertiliser per hectare and apples require 2 litres of fertiliser per hectare.
• Shivneel has a maximum of 1372 hours of labour and 280 litres of fertiliser.
• Shivneel must grow at least 18 hectares of apples and at least 16 hectares of rock melons.

Income predictions:

• For the current year, he expects to receive $1469 per hectare for his apples and $329 per hectare for his rock melons.
• He is unsure of the future income from apples, but he thinks that next year will be approximately $164.5 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: