Lecture21aa

# Lecture21aa - Lecture 1 LP Formulation Examples a Blending...

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Lecture 03/07/08 1. LP Formulation Examples a. Blending Problems b. Production Process Problems

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Blending Problem Gasoline A Gasoline B Blend 1 Blend 2 Octane Rating=120 Cost=\$2.75/gal 1000 gal. available Octane Rating=100 Cost=\$2.70/gal 1000 gal. available Octane Rating=115 Selling price=\$2.85/gal Octane Rating = 110 Selling price =\$2.75/gal
Definition of Decision Variables and Operating Rules • Let x ij = gal/day of raw gasoline j in blend i i=1,2; j=A,B Blending constraints 115 ) 100 ( x x x ) 120 ( x x x 1B 1A 1B 1B 1A 1A = + + + Fraction of Gas A in Blend 1 Fraction of Gas B in Blend 1 Octane Ratings of Gas Octane Rating of Blend 1

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Simplifying Blending Constraints Multiply each term by ) x x ( 115 x 100 120x 1B 1A 1B 1A + = + 1B 1A x 3 x = 110 ) 100 ( x x x ) 120 ( x x x 2B 2A 2B 2B 2A 2A = + + + Likewise for Blend 2 Simplifies to x 2A =x 2B 1B 1A x x +
Other Constraints 1000 x x 1000 x x 2B 1B 2A 1A + + Availability of First constraint can be rewritten 1000 x x 3 2B 1B +

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Lecture21aa - Lecture 1 LP Formulation Examples a Blending...

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