{ii} {iii} {iv} {V} Determine the decision variables, the objective function and the model constraints. [III] marks] Using a Spreadsheet model. determine the optimal solution that will generate maximum prots from current production. [1 [It marks] Given your answers in [ii] above, what would happen in case the company decides that each product must make up at 25% of the total units sold. What is the new level of prots? Show tabulated results and working. [20 marks] What Would happen if the prot contribution for chairs reaches $1 and subsequently when it reaches $21.13!}? Show tabulated results and working. [20 marks] From your answers in {ii}, you realise that fabrication time limits your ability to increase prots. Maybe We should acquire more of it. How much should We pay for additional time? [It] marks] 2. When normalizing the parameters for a ICobb Douglas Function1 prove that the utility is unique only Up to a monotonic transformation ifu = {13. [10 marks] 3. Maximisation: Solo's Furniture Company makes onlyr three kinds of fumitures (chairs1 desks and tables]. Each product requires some labor in the parts Fabrication department, the assembly department and the shipping department. The fumiture is sold through a local distributor who has Estimated the maximum potential sales for each prodUct in the next quarter. Finally1 the accounting department has provided some data showing the prot contributions on each product. The decision problem is to determine the product mix, that is, to maximise Solo's Fumitttre Company's prot for the quarter by choosing prodUction quantities for the chairs, desks and tables. The table below"r summarises the narameters ofthe roblems. Hours er Unit Department Chairs Desks Tables Hours Available 1,350 _'- 1,400 m- 1,500 Demand 3 31):} Pete ntial \