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

Information:

• Pencils require 3 hours of labour per box sold and biscuits require 18 hours of labour per box sold.
• Pencils require 59 m² of storage space per box sold and biscuits require 118 m² of storage space per box sold.
• Bradley has a maximum of 702 hours of labour and 6962 m² of storage space.
• Bradley must sell at least 11 boxes of biscuits and at least 18 boxes of pencils.

Income predictions:

• For the current year, he expects to receive $386 per box sold for his biscuits and $1395 per box sold for his pencils.
• He is unsure of the future income from biscuits, but he thinks that next year will be approximately $2790 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: