Optimizacion Lineal.docx

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𝑆𝑒𝑎 𝑥1 = 𝑐𝑎𝑛𝑡𝑖𝑑𝑎𝑑 𝑑𝑒 𝑙𝑖𝑏𝑟𝑜𝑠 𝑎 𝑝𝑟𝑜𝑑𝑢𝑐𝑖𝑟 𝑦 𝑥2 = 𝑐𝑎𝑛𝑡𝑖𝑑𝑎𝑑 𝑑𝑒 𝑟𝑒𝑣𝑖𝑠𝑡𝑎𝑠 𝑎 𝑝𝑟𝑜𝑑𝑢𝑐𝑖𝑟 𝑀𝑎𝑥 30000𝑥1 + 25000𝑥2 S.a 6𝑥1 + 5𝑥2 5𝑥1 + 7𝑥2 10𝑥1 + 4𝑥2

≤ 300 ≤ 350 ≤ 400

𝑥1 , 𝑥2 ≥ 0

Este problema tiene soluciones optimas multiples entre las cuales tenemos las siguientes: 𝑝𝑟𝑜𝑑𝑢𝑐𝑖𝑟 𝑥1 =

350 600 𝑑𝑒 𝑙𝑖𝑏𝑟𝑜𝑠 𝑦 𝑥2 = 𝑑𝑒 𝑟𝑒𝑣𝑖𝑠𝑡𝑎𝑠 17 17

𝑜 𝑝𝑟𝑜𝑑𝑢𝑐𝑖𝑟 𝑥1 =

400 13

𝑙𝑖𝑏𝑟𝑜𝑠 𝑦 𝑥2 =

300 13

𝑑𝑒 𝑟𝑒𝑣𝑖𝑠𝑡𝑎𝑠

Las dos soluciones generan una utilidad de 𝑧 = 1500000

𝑆𝑒𝑎 𝑥1 = 𝑐𝑎𝑛𝑡𝑖𝑑𝑎𝑑 𝑑𝑒 𝑏𝑖𝑙𝑙𝑒𝑡𝑒𝑟𝑎𝑠 𝑎 𝑝𝑟𝑜𝑑𝑢𝑐𝑖𝑟 𝑦 𝑥2 = 𝑐𝑎𝑛𝑡𝑖𝑑𝑎𝑑 𝑑𝑒 𝑐𝑖𝑛𝑡𝑢𝑟𝑜𝑛𝑒𝑠 𝑎 𝑝𝑟𝑜𝑑𝑢𝑐𝑖𝑟 𝑚𝑖𝑛 12000𝑥1 + 600𝑥2 S.a 6𝑥1 4𝑥1 𝑥1

3𝑥2 5𝑥2

≤ 180 ≤ 200 ≤ 40

𝑥1 , 𝑥2 ≥ 0

Este problema tiene soluciones optimas multiples entre las cuales tenemos las siguientes: 𝑝𝑟𝑜𝑑𝑢𝑐𝑖𝑟 𝑥1 = 0 𝑏𝑖𝑙𝑙𝑒𝑡𝑒𝑟𝑎𝑠 𝑦 𝑥2 = 60 𝑐𝑖𝑛𝑡𝑢𝑟𝑜𝑛𝑒𝑠 𝑜 𝑝𝑟𝑜𝑑𝑢𝑐𝑖𝑟 𝑥1 =

50 3

𝑏𝑖𝑙𝑙𝑒𝑡𝑒𝑟𝑒𝑎𝑠 𝑦 𝑥2 =

Las dos soluciones generan una utilidad de 𝑧 = 360000

80 3

𝑐𝑖𝑛𝑡𝑢𝑟𝑜𝑛𝑒𝑠

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