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Unformatted text preview: 35 55 30.00 X220 60 25 34.8 44 LP Formulation
FIRST requirement: • At least 45% of each barrel of regular must be ingredient A .
– (R1+ 2) is the total amount of crude blended to produce
R
Regular gas. This should contain at least 45% ingredient A, i.e.,
0.45 (R1+ 2) is the required minimum.
R
– 0.35 R1+
0.60 R2 is the amount of A in Regular gas after
blending
⇒ 0.35 R1+0.60 R2 > 0.45 (R1+R2)
can be simplified as:  0.10 R1 + 0.15 R2 > 0
45 LP Formulation
SECOND requirement:
• At most 50% of each barrel of economy must be
ingredient B .
– E1 +E2 is the total amount of crude blended to
produce Economy gasoline. This should contain
at most 50% of ingredient B, i.e.,
0.50 (E1+E2) is maximum amount allowed.
– 0.55 E1+ 0.25 E2 is the amount of ingredient
B in Economy gas after blending
⇒ 0.55E1+0.25E2 < 0.50(E1+E2)
can be simplified as:
0.05E1 – 0.25E2 < 0
46 LP Problem Formulation
Objective: Minimize total cost =
$30 R1 + $30 E1 + $34.80 R2 + $34.80 E2
subject to: R1 + R2 ≥ 25, 000 (Demand for Regular) E1 + E2 ≥ 32, 000 (Demand for Economy) −0.10 R1 + 0.15 R2 ≥ 0 (Ingredient A in Regular) 0.05 E1 − 0.25 E2 ≤ 0 (Ingredient B in Economy) R1, E1, R2 , E2 ≥ 0
47 Optimal Blending Solution
The least total cost is $1,783,600 by blending:
• 1,500 barrels of crude oil X100 and 10,000
barrels of crude oil X220 to produce Regular
• 2,666.67 barrels of crude oil X100 and
5,333.33 barrels of crude oil X220 to produce
Economy
All the demand on gasoline and minimum
requirements on ingredients are satisfied exactly.
48...
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 Spring '12
 TOMMYLAU

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