Extra Virgin is a producer of high-quality olive oil . The company buys raw olives directly from large agricultural companies and refines them into olive oil that it sells in the wholesale market. The company has a maximum input capacity of 150 tons of raw olives every day (or 54,750 short tons per year). But, the company cannot run at full capacity every day as it is required to shut down or reduce the capacity for maintenance periods every year, and it experiences the occasional mechanical problem. Then, the facility is expected to run at 90% capacity over the year (or on average 150 x 90% = 135 tons per day). Extra Virgin is planning to purchase its supply of raw olives from two primary growers, Supplier A and Supplier B. Purchase prices will not set until the orders are actually placed, so Extra Virgin will have to forecast purchase prices for the raw material and sales prices for the refined olive oil. For both suppliers, it is expected that the average yield of oil from the olives is 40%. Historical prices for the last 15 years are in the table below (note that year 15 is the most current year). Historical Price Data Oil Raw olive Average Price Index Index Average Price $/ton Marketing Year 2 3 4 15 16 7 18 9 125.7 192.4 242 240 284 242 280 347.2 436 442.8 461 582 508 438 434 $/ton 307.8 465 652.2 664.2 791.3 732 921 (1123 1297.3 1312 (1406 1664 1317.4 1172.4 (1334.4 10 11 12 13 14 15 Olive oil contains a number of fatty acids, some which are desirable in food products and others that are not. One desirable fatty acid is oleic acid. Extra Virgin produces high oleic oil for the wholesale market, and requires that the oleic acid content be a minimum of 75%. Olive oil also contains trace amounts of Linoleic. The market requires that that Linoleic content be a minimum of 15% and maximum of 21% The oleic acid and Linoleic content for the olives from the three suppliers is given in the table below. Supplier A B Oleic Acid 85% 70% Linoleic 9% 22% For both suppliers, it is expected that the average yield of oil from olives is 40%. Because the oleic acid and linoleic content varies across the suppliers, so does the price. It is expected that the cost of supply from the suppliers will be a percentage of the market average price of olives. Supplier A Cost as % of Average Market Price of raw olives 94% B 90% The company faces an additional variable production cost of $11/short ton and an estimated fixed cost of $1,790,000 over the upcoming production period. The company is asking you to provide a recommendation on the amount of raw material it should purchase from each supplier to minimize its cost of feedstock. Management is also looking for an analysis on the profitability of the company in the next production cycle. Suggested Approach This is a fairly complex problem. The following approach is suggested: Use the historical price data set as input to a time series forecast model in order to generate forecasted prices for the average price of olives, oil, and mash in the next production period. Use standard measures of error to decide between a three-period moving average model or an exponential smoothing model (with a = 0.2). Use the type of model for all three time series forecasts. That is, if you decide to use the moving average model, use a three-period moving average model to fit the relevant data for all three series. Don't use the moving average for one time series and the exponential smoothing model for another time series. Formulate a linear program to minimize the cost of raw olives. Use the average price of olives forecasted from the previous step in order to determine supplier prices. Perform a cost-volume-price analysis (review the handout entitled Cost-Volume-Profit Analysis for details) using the average cost per short ton average selling price per short ton. You can generate an effective cost per short ton by dividing the total cost of supply (from the linear program) by the total volume (that you assumed in the linear program). You can generate an effective selling price per short ton from the expected percentage yields and the forecasted average price of olive oil and mash. Because of the way that the contract is written, you can assume that the purchase of raw olives is a variable cost (you only purchase what you require). o Recall that the cost-volume-price analysis requires you to provide . an algebraic statement of the revenue function and the cost function, a detailed break-even chart that includes lines for the revenue and for the total cost, fixed cost, and variable cost a total of four lines), and a calculation break-even point expressed in number of short tons and percent of capacity. Management Report Prepare a written management report that includes, at a minimum, the following sections: Purpose of the Report Description of the Problem Methodology (which would include the model formulation) Findings or Results Recommendations or Conclusions . Be sure to address all relevant points, discuss any assumptions you are making, justify any modeling choices you have made (for example, the choice of time series forecast model), and highlight the following items in your report: . a forecast of the next production period's average price index for raw olives, olive oil, and olive mash, a recommendation for the optimal purchasing strategy from the various suppliers, a cost-volume-profit analysis using for the recommended purchase strategy and the forecasted olive oil and mash sales price, a discussion of the risks and uncertainties that are faced by the company, and an analysis and opinion on the profitability of the company in the next production period (accounting for the expected profit or loss and the inherent risks/uncertainties