Aggregate Planning at K-Corporation K-Corporation (K-Co) was a mid-sized manufacturer and distributor of domestic electrical appliances, primarily catering to the price-sensitive rural population in Australia. K-Co has operated a mid-sized factory since 1986. Currently, K-Co is hiring 50 employees, including Susan Wright. K-Co manufactured a wide range of electrical appliances for household use, including television signal boosters, transformers, FM radio kits, electronical ballasts, battery charges, and voltage regulators. Because of poor planning, K-Co made zero profit in the first 4 months of the financial year. Susan was assigned the task of preparing an aggregate plan for the flagship product R11. The sales of R11 products accounted for nearly 40% of the annual sales. Each unit of R11 was an assembly of one T0X unit and one P0Y unit. Each T0X unit requires two T1X1 components and three T1X2 components. Because of limited labour hours, the monthly production quantity cannot exceed the maximum monthly volume specified by the factory manager. The backorder cost is incurred for the finished goods (R11) but not for the components (T1X1, T1X2, P0Y) or the semi-assembly (T0X). At the end of 8th month, all of the demands must be met (no backorder at that time). Susan understood that she must devise a plan that maximises the profit-after-tax, by taking into account the setup cost, the production cost, the tax rate, the forecasted demand, the product structure, and the relevant considerations. Questions: 1) 2) 3) 4) How much is the maximal profit-after-tax? (35 marks) How does the optimal production plan look like? (25 marks) Can you identify any bottle neck by examining the optimal production plan? (10 marks) If K-Co purchases a new machine that costs $25,000 and immediately puts the new machine in operations, the production lead time for R11 would reduce to be negligible. Susan is wondering if such capital investment is worthy. Can you perform relevant analysis to assist Susan in making this decision? (30 marks) You must submit the EXCEL file (no other file is accepted) through blackboard. Type your explanations in textboxes. Hints: - Your EXCEL file should contain one worksheet dedicated for the \"long lead time\" scenario and another worksheet dedicated for the \"zero lead time\" scenario. The capital expenditure is tax deductible. Internal demands for each components are generated by the production of the finished goods or semi-assembly that the components are assembled into. For instance, a production of 100 units of R11 generates an internal demand of 100 units for T0X; a production of 130 units of T0X generates an internal demand of 260 units for T1X1 and an internal demand of 390 units for T1X2. Exhibit 1: Product Structure Diagram T0X (1) R11 T1X1 (2) T1X2 (3) P0Y (1) Exhibit 2: Forecasted Demand Month Deman d 1 800 2 350 3 300 4 750 5 300 6 450 7 350 8 400 Total 3700 Exhibit 3: On Hand Inventory and Maximum Monthly Volume Serial Number R11 T0X P0Y T1X1 T1X2 On Hand Inventory 100 240 340 500 600 Maximum Monthly Volume 1600 2000 2000 4000 4000 Exhibit 4: Associated Costs Serial Number R11 T0X P0Y T1X1 T1X2 - Production Cost 100 65 35 5 15 Holding Cost =100*0.05=5 Holding cost per unit per month is 5% of the production cost for all items. Backorder cost is $50 per unit per month for the finished good of R11. Exhibit 5: Other Considerations - Shortage of component supply is not allowed. All demands must be met at the end of 8 th month (i.e., the end of the financial year). Production lead time for T0X, P0Y, T1X1, and T1X2 is negligible, however, that for R11 is 1 month (before the new machine is in operations). Selling price of R11 is $500 per unit. Marginal tax rate is 0% if profit-before-tax is less than $100,000 and increases to 20% afterwards