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

Information:

• Milk require 3 hours of labour per box sold and magazines require 30 hours of labour per box sold.
• Milk require 6 m² of storage space per box sold and magazines require 2 m² of storage space per box sold.
• Foley has a maximum of 1890 hours of labour and 996 m² of storage space.
• Foley must sell at least 15 boxes of magazines and at least 20 boxes of milk.

Income predictions:

• For the current year, he expects to receive $1575 per box sold for his magazines and $625 per box sold for his milk.
• He is unsure of the future income from magazines, but he thinks that next year will be approximately $6250 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: