Lecture 2 - LP Model Patterns Exercise: Solve the LP model...

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LP Model Patterns
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Exercise: Solve the LP model Max Z = 10 x 1 + 20 x 2 st: -x 1 + 2 x 2 10 x 1 + x 2 8 5 x 1 + 3 x 2 30 x 1 0, x 2 0
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Assumptions of LP: Note the following assumptions that we are making about the following LP sample formulation: Proportionality of resource use and unit profits; Additivity of terms; Divisibility of activities into the fractional levels; Certainty of the problem parameters.
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Various LP Problems Agricultural Planning 1. 3 farms with the following resources: Farm Usable Water land (acre) availability (acre-ft) 1 400 600 2 600 800 3 300 375
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Agricultural Planning cont’d 2. Crops under consideration are sugar beets, cotton, and sorghum with the following characteristics: Crop Max. quota Water Net return (acres) acre-ft/acre $/acre Sugar 600 3 400 Cotton 500 2 300 Sorghum 325 1 100
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Agricultural Planning cont’d 3. The governmental regulations require that at each farm 4. For labor distribution, every farm must have the same percentage of land planted. Area planted 60% Total area
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Agricultural Planning cont’d LP Model Define x i as the acres of land allocated to a crop as follows: Farm 1 2 3 1 x 1 x 2 x 3 Crop 2 x 4 x 5 x 6 3 x 7 x 8 x 9
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Agr. model cont’d Max Z= 400( x 1 +x 2 +x 3 )+300 ( x 4 +x 5 +x 6 )+100 ( x 7 +x 8 +x 9 ) st: Land x 1 + x 4 + x 7
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This document was uploaded on 11/04/2011 for the course MME 414 at Miami University.

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Lecture 2 - LP Model Patterns Exercise: Solve the LP model...

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