SECTION II Question 1 Many of today's digital or electronic devices and equipment cannot function without the use of highly complex interconnected network of generally microscopic electronic components. Nano Semicon is one of the leading contract manufacturer of integrated circuits (or IC chips) manufacturer in the region. The worldwide shortage of these IC chips has put pressure on IC chip manufacturers ever increasing demands. Nano Semicon currently manages to cope with this upsurge in IC chips consumption. Nano Semicon has already converted much of its manufacturing facility into a highly automated factory, employing robotics and artificial intelligence to handle most of the repetitive tasks. However, the factory still needs some workers to be working in shifts such as process engineers, technical support personnel, software programmers and quality control inspectors. The factory works on a 24/7 five-shift basis. The full cycle of operations starts at 7am (or 0700) and ends at 7am the next day. This cycle is divided into 9 periods, each consisting of a two- hour duration. For example, the first two-hour period of the cycle lasts from 0700 to 0900. The details of the breakdown of the time periods as well as the minimum number of workers required per time period are given in Table 1 below. As workers per shift are given different tasks to perform, their wages per worker varies from shift to shift. The Production Manager, together with the Human Resource Manager had worked out the cost per worker per shift. These are also given in Table 1 below. The "A" symbols in Table 1 indicate the number of time periods that each shift of workers must work. For example, Shift 1 workers are required to work from 0700 to 1500. (Time includes lunch of 30 minutes at 12.30pm). Shift Time Period Minimum number of 2 3 Workers Required 0700 - 0900 32 1900 - 1100 70 1100 - 1300 62 1300 - 1500 55 1500 - 1700 65 1700 - 1900 62 1900 - 2100 70 2100 - 2300 35 2300 - 0700 15 Wage per workerBased on the given information: (a) (b) (d) (E) State three (3) practical assumptions applicable to this linear programming in problem. Your assumptions must be specific to the LP problem. (Assumptions = If: marks} Develop a linear programming (LP) model to minimise the worker costs of Nano Semicon for one cycle of operations (T on Day 1 to T on Day 2]. Your model must be in the form of algebraic equations and inequalities where appropriate. Dene clearly your Decision Variables. lDbjective function and Constraints. (LP model = 1'? marks) Solve the LP model using the Excel Solver and present your Answer and Sensitivity Reports in their original formats generated by the Solver. [Answer Report = 3 marks) (Sensitivity Report = 3 marks) Referring to any constraint with a non-zero Shadow Price in your Sensitivity Report, explain the term \"Shadow Price\". Illustrate using an example from your Sensitivity Report how a non-zero Shadow Price works and state the condition(s) under which it can be applied. (Explanation = 3 marks) [lustration of Shadow Price = 45 marks) [Condition for application = 3 marks) Due to the difficulty of getting workers for Shift 5 (commonly known as the \"graveyard shift\"), the management of Nano Semicon has decided to pay more wages to attract more workers to work in that shift. As a result, the wage per worker is increased to $T. Determine the change [if any} in the objective function value due to the increase in the wage per worker for Shift 5 and obtain the new objective function solution (i.e. new Z)? (4 marks] Question 2 (a) Chris and Aziz are two budding entrepreneurs operating a small grocery chain in Singapore. Their company, Aztec Prima recently secured a distributorship for a unique yoghurt drink from Taiwan manufacturer. The myriad flavours and pleasant taste of the drink quickly won over the taste buds among the old and young. Following the reasonable success of the yoghurt drink in Singapore, both business partners are eyeing the larger market in Malaysia. They have the following alternatives to consider, viz: Option 1 - test in Johor Bahru (JB) Option 2 - do not test in Johor Bahru (JB) For Option 1, there is 80% chance of success and 20% chance of failure. If Option 1 (test in JB) is successful, there are 2 choices: Choice A - launch in Malaysia with the success and failure and expected net revenue as shown in Table 2.1: Launch in Other Malaysian cities Outcome Probability Net Revenue per Month Success 0.85 $420,000 Failure 0.15 $20.000 Table 2.1 - Launch in other Malaysian cities Choice B - do not launch in Malaysia (i.e. focus in JB) with an expected net revenue of $120,000 per month. If Option 1 (test in JB) is a failure (i.e. 20%), there are 2 choices: Choice C - launch in Malaysia with the success and failure and expected net revenue as shown in Table 2.2: Launch in Other Malaysian cities Outcome Probability Net Revenue per Month Success 0.10 $400,000 Failure 0.90 $22,000 Table 2.2 - Launch in other Malaysian cities Choice D- do not launch in Malaysia (i.e. focus in JB) with an expected net revenue of $20,000 per month.For Option 2 (do not test in JB), they have two choices: Choice E - launch in Malaysia with the success and failure and expected net revenue as shown in Table 2.3: Launch in Other Malaysian cities Outcome Probability Net Revenue per Month Success 0.55 $420,000 Failure 0.45 $50,000 Table 2.3 - Launch in other Malaysian cities Choice F - do not launch in Malaysia (i.e. focus in JB) with an expected net revenue of $170,000 per month. (i) Based on the above information, define a Decision Tree, showing clearly the Decision nodes, Event Nodes and Terminal Nodes and related net revenues. Label clearly all branches, Decision nodes and Event nodes in your Decision Tree diagram. (Decision Tree = 10 marks) (Labelling clarity = 3 marks) (ii) Compute the Expected Values (EVs) at each of the Event nodes in your Decision Tree. (EVs = 8 marks) (iii) State the decision that the partners should take at the beginning based on the maximum EV value. (Decision at Node 1 = 4 marks)Question 2 (b) Alan Gomez is the GM of a fairly successful enterprise selling hardware accessories used mainly in DIY tasks such as bolts and nuts, screws, sealants, taps and toilet flushing systems, pipes and tubing's, power drills, etc. For the past 5 years. Alan has been performing sales forecasting of his 3 most saleable products based on his experience and "feel" of the prospects for the DIY business. Recently, he attended a course in Marketing where he learned some of the common forecasting methods which are directly relevant to his business. Being busy with plans to start a new DIY outlet, Alan directed you as the Marketing Manager to conduct a forecasting analysis of the company's monthly sales for a reputable brand of power drills using the last 15 months of sales data. The data are presented below: Units sold per month 123 95 106 75 115 56 75 134 110 93 102 12 72 13 89 14 112 15 95 Table 2.3 - Monthly sales (units) of Power Drills (i) Plot a graph of the above data and explain why it may not be appropriate to apply the Time Series method of forecasting to analyse the monthly sales of power drills. (Graph= 2 marks) (Explanations = 2 marks)(ii) Determine and tabulate the forecasts. related errors and squared errors using the Weighted Moving Average (WLW) method and the Exponential Smoothing (ES) method. Use the information given below. Round off all forecasts to rim (2) decimal places. You are required to provide the manual calculations of the rst three (3) forecasts in each of the forecasting methods. 'WMV method: ' K = 3 ' Weight for the most recent data = 4:"? . Weight for the next most recent data = 2:"? ' Weight for the least recent data = 1;"? ES method: ' at = {1.3 . Assume F1 = 123 units of power drills sold per month (Forecasts and errors from both methods: 3 marks) (iii) Which of the min (2) methods of forecasting provides a better forecast accuracy.r based on the MSE'? State your reason(s]. [2 marks) (iv) Discuss briey.F three (3) practical factors which can cause forecast errors in the sales of power drills. [l5 marks} ---- END OF ASSIGWENT