3.2 Question Generator - Uzoma's Bakery
Introduction:
This activity requires you to use linear programming to model the constraints Uzoma 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:
Uzoma owns a bakery and makes cup cakes and filled rolls. Use the information below to write a report for Uzoma making recommendations as to how many batches of each type he should make.

Information:

• Cup cakes require 4 hours of labour per batch and filled rolls require 14 hours of labour per batch.
• Cup cakes require 2 kilograms of flour per batch and filled rolls require 4 kilograms of flour per batch.
• Uzoma has a maximum of 1008 hours of labour and 336 kilograms of flour.
• Uzoma must make at least 16 batches of filled rolls and at least 14 batches of cup cakes.

Income predictions:

• For the current year, he expects to receive $421 per batch for his filled rolls and $1151 per batch for his cup cakes.
• He is unsure of the future income from filled rolls, but he thinks that next year will be approximately $4028.5 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: