TourneSol Canada, Ltd. is a producer of high-quality sunflower oil. The company buys raw sunflower

seeds directly from large agricultural companies and refines the seeds into sunflower oil that it sells

in the wholesale market. As a by-product, the company also produces sunflower mash (a paste

made from the remains of crushed sunflower seeds) that it sells into the market as a base product

for animal feed.

The company has a maximum input capacity of 150 short tons of raw sunflower seeds every day (or

54,750 short tons per year). Of course, 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. The facility is expected to run at 90% capacity over the year (or

on average 150 x 90% = 135 short tons per day).

TourneSol is planning to purchase its supply of raw sunflower seeds from three primary growers,

Supplier A, Supplier B, and Supplier C. Purchase prices will not be set until the orders are actually

placed so TourneSol will have to forecast purchase prices for the raw material and sales prices for

the refined sunflower oil and mash. The contract is written such that TourneSol is only required to

commit to 70% of total capacity upfront. 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).

Historical Price Data
Marketing Year	Seed Average Price Index $/short ton	Oil Average Price Index $/short ton	Mash Average Price Index $/short ton
1	127.7	317.8	63
2	192.4	465	87
3	242	662.2	105
4	242	668.2	111
5	274	791.3	124
6	242	732	108
7	290	951	134
8	347.2	1123	153
9	436	1297.3	193
10	422.8	1312	187
11	466	1416	193
12	582	1664	247
13	508	1317.4	242
14	428	1182.4	197
15	434	1334.4	210

Sunflower oil contains a number of fatty acids, some of which are desirable in food products and

others that are not. One desirable fatty acid is oleic acid. TourneSol produces high oleic oil for the

wholesale market and requires that the oleic acid content be a minimum of 77%. Sunflower oil also

contains trace amounts of iodine. The market requires that iodine content be a minimum of 0.78%

and a maximum of 0.88%

The oleic acid and iodine content for the sunflower seeds from the three suppliers is given in the

table below.

Supplier Oleic Acid Iodine

A 72% 0.95%

B 82% 0.85%

C 65% 0.72%

For all three suppliers, it is expected that the average yield of oil from the seeds is 30%. There is no

net loss of material, so the yield of mash from the same supply is expected to be 70%.

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 seeds.

Supplier Cost as % of Average Market Price of Seed

A 85%

B 100%

C 90%

The company faces an additional variable production cost of $10/short ton and an estimated fixed

cost of $1,750,000 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 of the profitability of the company in the next production

cycle.

Suggested Approach

This is a fairly complex problem. The following approach is suggested:

1- 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 sunflower seeds, 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 = 0.2). Use the type ofmodel 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.

Dont use the moving average for one time series and the exponential smoothing model for

another time series.

2- Formulate a linear programming to minimize the cost of raw sunflower seeds. Use the

average price of seeds forecasted from the previous step in order to determine supplier

prices.

3- Perform a cost-volume-price analysis (review the handout entitled Cost-Volume-Profit

Analysis for details) using the average cost per short ton and average selling price per short

ton.

o 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).

o You can generate an effective selling price per short ton from the expected

percentage yields and the forecasted average price of sunflower oil and mash.

o Because of the way that the contract is written, you can assume that the purchase of

raw sunflower seeds 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 the number of short tons and percent of

capacity.