3. Maximisation: Solo's Furniture Company makes only three kinds of furnitures (chairs, desks and tables). Each product requires some labor in the parts fabrication department, the assembly department and the shipping department. The furniture is sold through a local distributor who has Estimated the maximum potential sales for each product in the next quarter. Finally, the accounting department has provided some data showing the profit contributions on each product. The decision problem is to determine the product mix, that is, to maximise Solo's Furniture Company's profit for the quarter by choosing production quantities for the chairs, desks and tables. The table below summarises the parameters of the problems. Hours per Unit Department Chairs Desks Tables Hours Available Fabrication 4 6 2 1,850 Assembly 3 5 7 2.400 Shipping 3 2 4 1,500 Demand 360 300 100 Potential Profit $15 $24 $18(i) Determine the decision variables, the objective function and the model constraints. [10 marks] (1i) Using a spreadsheet model, determine the optimal solution that will generate maximum profits from current production. [10 marks] (iii) 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 profits? Show tabulated results and working. [20 marks] (iv) What would happen if the profit contribution for chairs reaches $16.00 and subsequently when it reaches $21.00? Show tabulated results and working. [20 marks] (v) From your answers in (1i), you realise that fabrication time limits your ability to increase profits. Maybe we should acquire more of it. How much should we pay for additional time? [10 marks]