# A Blending Problem

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```					A Blending Problem

COSC643

Dr. Sungchul Hong
Agri-Pro
• Agri-Pro is a company that sells agricultural
products to farmers in a number of states.
• One service it provides to customer is custom
feed mixing, whereby a farmer can order a
specific amount of livestock feed and specify the
amount of corn, grain, and minerals the feed
should contain.
• This is an important service because the proper
feed for various farm animals changes regularly
depending on the weather, pasture conditions,
and so on.
Agri-Pro
• Agri-Pro stocks bulk amounts of four types of
feeds that it can mix to meet a given
customer’s specifications.
Agri-Pro

Minimum
Feed1        Feed2      Feed3      Feed4       Req'd Amnt
Nutrient
Corn                   30.0%       5.0%      20.0%       10.0%        20.0%
Grain                  10.0%      30.0%      15.0%       10.0%        15.0%
Minerals               20.0%      20.0%      20.0%       30.0%        15.0%

Cost Per 1,000 lbs \$ 250.00 \$ 300.00 \$ 320.00 \$ 150.00

Agri-Pro has just received an order from a local chicken farmer for 8,000 pounds of
feed. The farmer wants this feed to contain at least 20% corn, 15% grain, and 15%
minerals.
Formulation
• X1 = amount of feed 1 in thousands of pounds
to use in the mix.
• X2 = amount of feed 2 in thousands of pounds
to use in the mix.
• X3 = amount of feed 3 in thousands of pounds
to use in the mix.
• X4 = amount of feed 4 in thousands of pounds
to use in the mix.
Objective Function
• MIN: 250X1 + 300X2 + 320X3 + 150X4
Constratint
• X1 + X2 + X3 + X4 = 8
• (0.30X1 + 0.05X2 + 0.20X3 +0.10X4)/8 >= 0.20
– Min % of corn required
• (0.10X1 + 0.30X2 + 0.15X3 + 0.10X4)/8 >= 0.15
– Min % of grain required
• (0.20X1 + 0.20X2 + 0.20X3 + 0.30X4)/8 >= 0.15
– Min % of minerals required
• X1, X2, X3, X4 >= 0

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 views: 7 posted: 8/24/2012 language: English pages: 7