Quantitative Math 1. a. Provide the network representation for the above transportation problem/ Supply Demand $35 / ton North Location: 35 tons $29 / ton Plant 1: 50 tons $40 / ton $37 / ton Plant 2: 50 tons South Location: 55 tons $38 / ton $44 / ton West Location: 10 tons b. Define the decision variables 𝐿𝑒𝑡: { 𝑖 = 𝑛𝑢𝑚. 𝑜𝑓 𝑃𝑙𝑎𝑛𝑡; 𝑖 = {1,2}, 𝑤ℎ𝑒𝑟𝑒 𝑖1 = 𝑃𝑙𝑎𝑛𝑡 1, 𝑖2 = 𝑃𝑙𝑎𝑛𝑡 2 𝑗 = 𝑛𝑢𝑚. 𝑜𝑓 𝑙𝑜𝑐𝑎𝑡𝑖𝑜𝑛𝑠; 𝑗 = {1,2,3}, 𝑤ℎ𝑒𝑟𝑒 𝑗1 = 𝑁𝑜𝑟𝑡ℎ, 𝑗2 = 𝑆𝑜𝑢𝑡ℎ, 𝑗3 = 𝑊𝑒𝑠𝑡 𝑇ℎ𝑒𝑟𝑒𝑓𝑜𝑟𝑒, 𝑥𝑖𝑗 = 𝑡𝑜𝑛𝑠 𝑜𝑓 𝑎𝑙𝑢𝑚𝑖𝑛𝑢𝑚 𝑚𝑜𝑣𝑒𝑑 𝑓𝑟𝑜𝑚 𝑝𝑙𝑎𝑛𝑡 𝑖 𝑡𝑜 𝑙𝑜𝑐𝑎𝑡𝑖𝑜𝑛 𝑗 Quantitative Math In detail: 𝑥11 = 𝑡𝑜𝑛𝑠 𝑜𝑓 𝑎𝑙𝑢𝑚𝑖𝑛𝑢𝑚 𝑚𝑜𝑣𝑒𝑑 𝑓𝑟𝑜𝑚 𝑝𝑙𝑎𝑛𝑡 1 𝑡𝑜 𝑙𝑜𝑐𝑎𝑡𝑖𝑜𝑛 1 (𝑁𝑜𝑟𝑡ℎ) 𝑥12 = 𝑡𝑜𝑛𝑠 𝑜𝑓 𝑎𝑙𝑢𝑚𝑖𝑛𝑢𝑚 𝑚? ...
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