This is a operations research question. Please take your time when answering the questions no rush and explain the answer so I can better understand The notes are stored on Google Drive and Dropbox Link 1 https://drive.google.com/file/d/18vTeSACKdXbaKvY5WR_9idk2Db7hvqpm/view?usp=drivesdkLink 2 https://www.dropbox.com/s/hy939603f1ng4f1/Operation%20Research%202015%204%20.pdf?dl=0

Question 4 A. The Thrill Company wants to predict their sales for the first five months of the year 2016. MONTH Actual Sales Jan 15 Feb 10 Mar 12 Apr 15 May 20 Jun 18 i. Use the three-month moving average to forecast the demand from April to July in the table above. ii. Use the three-month weighted moving average to forecast the demand from April to July in the table above; using the weights 0.45, 0.35 and 0.20. iii. Given an alpha (a) value of 0.35, use the exponential smoothing method of forecasting to predict the demand from February to July in the table above. iv. Use the Mean Absolute Deviation (MAD) to compare the two methods and state which is the most efficient one to use. v. Explain what is meant by seasonal variation and state how this variation could impact actual demand and the prediction on sales in an organization. B. The Pentium Company makes three types of pens: ballpoints, mechanical pencils and fountain pens. These are made from plastic, chrome and steel and the table gives the ounces of each of these ingredients that are used to make one pen. The company also uses labour, packaging and quality control techniques in the production process and the profitability of these pens, shown in the table are derived from the accounting process after all inputs are taken into account. For example, plastic cost $5.00 per ounce and this is taken into account to get the profit. Ballpoints Mechanical Fountain Available Pencils Pens (OZs) Profit per unit $3 $3 $5 Plastic 1.2 1.7 1.2 1,000 Chrome 0.8 0 2.3 1,200 Stainless Steel 2 3 4.5 2,000 i. Write the decision variables that will be used in the model and state the decision that the manager must make. ii. Write the objective function and state clearly what Pentium's objective is. iii. Write down all the constraints that should be used to solve the problem presented. iv. Explain what the solution would mean in terms of the decision variables and the objective function