Scenario

Double Olive Oil. Ltd. 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 180 short tons of raw Olives every day (or 65700 short tons per year). Of course the company cannot run at full capacity every day as it is required to shut down or reduce capacity for maintenance periods every year, and it experiences the occasional mechanical problem. The facility is expected to run at 90% capacity over the year (or on average 180 x 90% = 162 short tons per day).

Double Olive Oil is planning to purchase its supply of raw Olives from three primary growers, Supplier A, Supplier B, and Supplier C. Purchase prices will not set until the orders are actually placed so Double Olive Oil will have to forecast purchase prices for the raw material and sales prices for the refined Olive oil. The contract is written such that Double Olive Oil is only required to commit to 80% of total capacity up front. Any amounts over that can be purchased only as required for the same price. Historical prices for the last 15 years are in the table below (note that year 15 is the most current year).

Marketing Year	Olive Average Price Index $/short ton	Oil Average Price Index $/short ton
1	162.7	289.8
2	174.4	457
3	214	644.2
4	222	636.2
5	256	763.3
6	224	704
7	262	913
8	339.2	1015
9	418	1269.3
10	444.8	1304
11	453	1378
12	574	1636
13	520	1309.4
14	425	1144.4
15	428	1306.4

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. Double Olive Oil produces high oleic oil for the wholesale market and requires that the oleic acid content be a minimum of 78%. Olive oil also contains trace amounts of iodine. The market requires that that iodine content be a minimum of 0.77% and maximum of 0.87%

The oleic acid and iodine content for the Olives from the three suppliers is given in the table below.

Supplier	Oleic Acid	Iodine
A	69%	0.85%
B	74%	0.70%
C	84%	0.92%

Because the oleic acid and iodine content varies across the three 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	Cost as % of Average Market Price of Olive
A	70%
B	65%
C	80%

The company faces an additional variable production cost of $10/short ton and an estimated fixed cost of $1,020,000 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:

• 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.
  • 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).

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.