Question 1
This question is about the application of linear programming (LP). Part (b) is a continuation of Part (a), and Part (c) is not related to Parts (a) and (b).
 (A) OneHealth is a leading manufacturer of dietary supplements based in Singapore. The company specializes in producing high-quality health supplements tailored to meet various health needs, such as improving immune function, enhancing energy levels, and supporting overall well-being. As part of its commitment to quality and efficiency, OneHealth Pte Ltd. focuses on optimizing its production processes to minimize costs and maximize resource utilization. The company adheres to stringent health and safety regulations set by Singapore’s Health Sciences Authority (HSA), ensuring product quality and consumer safety.
The company aims to launch two new health supplements: Supplement Andes and Supplement Brave, which are made of different compositions of vitamin W and mineral X as shown in Table 1.
Table 1. The composition of Supplement Andes and Brave
| Supplement | W (%) | X (%) |
|---|---|---|
| Andes | 20 | 50 |
| Brave | 40 | 20 |
The following table shows the supply and cost information for vitamin W and mineral X.
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Table 2. Factual information on vitamin W and mineral X
| Resource | Weekly Supply (kg) | Cost ($ per kg) |
|---|---|---|
| W | 500 | 30 |
| X | 600 | 40 |
The marketing team has forecasted that the minimum weekly market demand for Andes and Brave is at least 500kg and 600kg, respectively. Also, a local department store has placed a confirmed total order of 1200 kg for Andes and Brave supplements, in any combination. The production team has also advised that for better utilization and load balancing of machines, for every kg of Andes tablets produced, at most Y kg of Brave tablets are produced (Y > 0).
You are required to state qualitatively the objective, decision variables and constraints. Then apply LP modelling to formulate the problem. Please limit the answer to within two pages.
(32 marks)
(b) Based on your formulation in Part (a), solve it using the LP graphical solution procedure. Show the possible optimal solutions and their corresponding condition (e.g., different values of Y).
(28 marks)
 (C) You are engaged as a motivational speaker for a youth congress. Being trained in Linear Programming (LP), you have consulted widely for a variety of enterprises in Singapore. Using no more than 400 words, prepare an engaging speech to motivate a group of secondary school students to approach decision-making using LP.
Using GenAI tools such as ChatGPT to generate material for work submitted for assessment, without any form of editing or acknowledgement, resulting in high Turnitin AI% will attract marks deduction and will be investigated as a plagiarism offence.
(40 marks)
