3.2 Question Generator - Ian's Bakery
Introduction:
This activity requires you to use linear programming to model the constraints Ian has for his bakery 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:
Ian owns a bakery and makes gingerbread men and rocky roads. Use the information below to write a report for Ian making recommendations as to how many batches of each type he should make.

Information:

• Gingerbread men require 3 hours of labour per batch and rocky roads require 27 hours of labour per batch.
• Gingerbread men require 42 kilograms of flour per batch and rocky roads require 3 kilograms of flour per batch.
• Ian has a maximum of 4617 hours of labour and 1638 kilograms of flour.
• Ian must make at least 14 batches of rocky roads and at least 18 batches of gingerbread men.

Income predictions:

• For the current year, he expects to receive $1566 per batch for his rocky roads and $1216 per batch for his gingerbread men.
• He is unsure of the future income from rocky roads, but he thinks that next year will be approximately $10944 per batch.

As you write your report take care to clearly communicate your findings using appropriate mathematical statements. Include graphs, equations, and relevant calculations.

Answer: