3.2 Question Generator - Ian's Shop
Introduction:
This activity requires you to use linear programming to model the constraints Ian has for his shop 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 shop and sells pens and milk. Use the information below to write a report for Ian making recommendations as to how many boxes of each type he should sell.

Information:

• Pens require 9 hours of labour per box sold and milk require 3 hours of labour per box sold.
• Pens require 235 m² of storage space per box sold and milk require 47 m² of storage space per box sold.
• Ian has a maximum of 513 hours of labour and 11045 m² of storage space.
• Ian must sell at least 10 boxes of milk and at least 19 boxes of pens.

Income predictions:

• For the current year, he expects to receive $1313 per box sold for his milk and $1680 per box sold for his pens.
• He is unsure of the future income from milk, but he thinks that next year will be approximately $336 per box sold.

As you write your report take care to clearly communicate your findings using appropriate mathematical statements. Include graphs, equations, and relevant calculations.

Answer: