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

Information:

• Snap backs require 2 hours of labour per box sold and bubble gum require 8 hours of labour per box sold.
• Snap backs require 10 m² of storage space per box sold and bubble gum require 5 m² of storage space per box sold.
• Dan has a maximum of 432 hours of labour and 550 m² of storage space.
• Dan must sell at least 10 boxes of bubble gum and at least 8 boxes of snap backs.

Income predictions:

• For the current year, he expects to receive $1635 per box sold for his bubble gum and $1083 per box sold for his snap backs.
• He is unsure of the future income from bubble gum, but he thinks that next year will be approximately $541.5 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: