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DATA ENVELOPMENT ANALYSIS 195

changes in supply or demand, management also indicated that 25 000 pounds of tiger shrimp
must be in storage at the end of week 4. Determine the optimal buying-storing-selling strategy
for ASC. What is the projected four-week profit?
10 Romans Food Market, located in Italy, carries a variety of speciality foods from around
the world. Two of the store’s leading products use the Romans Food Market name:
Romans Regular Coffee and Romans DeCaf Coffee. These coffees are blends of
Brazilian Natural and Colombian Mild coffee beans, which are purchased from a
distributor. Because Romans purchases large quantities, the coffee beans may be
purchased on an as-needed basis for a price 10 per cent higher than the market price the
distributor pays for the beans. The current market price is E0.47 per kilo for Brazilian
Natural and E0.62 per kilo for Colombian Mild. The compositions of each coffee blend
are as follows:

Blend
Bean Regular DeCaf
Brazilian Natural 75% 40%
Colombian Mild 25% 60%

Romans sells the Regular blend for E3.60 per kilo and the DeCaf blend for E4.40 per kilo.
Romans would like to place an order for the Brazilian and Colombian coffee beans that will
enable the production of 1000 kilos of Roman Regular coffee and 500 kilos of Roman
DeCaf coffee. The production cost is E0.80 per kilo for the Regular blend. Because of the
extra steps required to produce DeCaf, the production cost for the DeCaf blend is E1.05
per kilo. Packaging costs for both products are E0.25 per kilo. Formulate a linear
programming model that can be used to determine the kilos of Brazilian Natural and
Colombian Mild that will maximize the total contribution to profit. What is the optimal
solution and what is the contribution to profit?
11 Seastrand Oil Company produces two grades of fuel: regular and high octane. Both
fuels are produced by blending two types of crude oil. Although both types of crude oil
contain the two important ingredients required to produce both fuels, the percentage of
important ingredients in each type of crude oil differs, as does the cost per litre. The
percentage of ingredients A and B in each type of crude oil and the cost per fuel are
shown.

Crude oil 1
Crude Oil Cost Ingredient A Ingredient B 60% ingredient B

1 E0.10 20% 60% !
2 E0.15 50% 30%

Each litre of regular fuel must contain at least 40 per cent of ingredient A, whereas each fuel of
high octane can contain at most 50 per cent of ingredient B. Daily demand for regular and
high-octane fuel is 800 000 and 500 000 litres, respectively. How many litres of each type of
crude oil should be used in the two fuels to satisfy daily demand at a minimum cost?

12 Frandec Company manufactures, assembles and rebuilds material handling equipment
used in warehouses and distribution centres. One product, called a Liftmaster, is
assembled from four components: a frame, a motor, two supports and a metal strap.

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