5. Integrated problem (5 marks) Technico is a new manufacturer company that plans to start its operations soon. It produces one model of high-end product using a production system as illustrated in the figure below. The figure shows two different processing departments each consisting of similar machines that are operated by an operator. Each operator can handle up to five machines in each department. Machine A Supplier Machine A2 Machine Bi Customer Machine B2 Inventory A Inventory B Department A Department B Machines in Department B can only process the outputs from Department A that are released to Department B (if not held at Inventory A). Below is the key data of processes in the two departments: Key data Price per machine Annual production capacity per machine (in units) Production cost per unit Overtime cost per unit Department A $750,000 Department B $1,000,000 40,000 50,000 $20 $40 $40 $50 $5 Inventory cost per unit $10 The sales forecast has determined demand projections over the next four years as follows: Year 1 (100,000 units), Year 2 (120,000 units), Year 3 (140,000 units), and Year 4 (160,000 units). Assume that daily demand remains stable over the year, and the company operates 7 days a week. Technico has identified a raw materials supplier that is ready to meet its demand, and it is determined for not having any backorder in meeting the annual demands. Technico's management team is discussing the production capacity plan of the factory. For example, how many machines it needs to purchase over the four years, whether it should follow the predicted demand patterns (by gradually adding more machines) or produce ahead of the demand and keep stock of finished product. Overtime is also another option that is considered. Propose the production capacity plan of each department to meet the demand forecast at the lowest total cost (which must include the cost of purchasing the machines) over these four years. Explain clearly the logic behind your production plan; i.e. the number of machines that Technico should invest in, the amount of overtime hours and inventory units (if any), and the machines' utilisation rate. It is recommended that you use table(s) in your quantitative analysis to support your answers and demonstrate your understanding of the relevant operations management theories or concepts.