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

Information:

• Soft drinks require 6 hours of labour per box sold and bubble gum require 2 hours of labour per box sold.
• Soft drinks require 14 m² of storage space per box sold and bubble gum require 2 m² of storage space per box sold.
• River has a maximum of 420 hours of labour and 924 m² of storage space.
• River must sell at least 7 boxes of bubble gum and at least 16 boxes of soft drinks.

Income predictions:

• For the current year, he expects to receive $1853 per box sold for his bubble gum and $819 per box sold for his soft drinks.
• He is unsure of the future income from bubble gum, but he thinks that next year will be approximately $273 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: