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

Information:

• Sunglasses require 15 hours of labour per box sold and pens require 20 hours of labour per box sold.
• Sunglasses require 115 m² of storage space per box sold and pens require 92 m² of storage space per box sold.
• Jock has a maximum of 1500 hours of labour and 10580 m² of storage space.
• Jock must sell at least 5 boxes of pens and at least 4 boxes of sunglasses.

Income predictions:

• For the current year, he expects to receive $1885 per box sold for his pens and $415 per box sold for his sunglasses.
• He is unsure of the future income from pens, but he thinks that next year will be approximately $332 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: