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

Information:

• Bottles of water require 2 hours of labour per box sold and sunglasses require 8 hours of labour per box sold.
• Bottles of water require 6 m² of storage space per box sold and sunglasses require 8 m² of storage space per box sold.
• Cody has a maximum of 640 hours of labour and 1104 m² of storage space.
• Cody must sell at least 18 boxes of sunglasses and at least 12 boxes of bottles of water.

Income predictions:

• For the current year, he expects to receive $1759 per box sold for his sunglasses and $529 per box sold for his bottles of water.
• He is unsure of the future income from sunglasses, but he thinks that next year will be approximately $2116 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: