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

Information:

• Pens require 97 hours of labour per box sold and butter require 776 hours of labour per box sold.
• Pens require 565 m² of storage space per box sold and butter require 113 m² of storage space per box sold.
• Layne has a maximum of 75272 hours of labour and 63845 m² of storage space.
• Layne must sell at least 10 boxes of butter and at least 8 boxes of pens.

Income predictions:

• For the current year, he expects to receive $529 per box sold for his butter and $1033 per box sold for his pens.
• He is unsure of the future income from butter, but he thinks that next year will be approximately $8264 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: