35 r1060 r2 045 r1r2 can be simplified as 010 r1

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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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