Question

Transhipment Nodes Let index plants, index markets ai supply at plant i bj demand at market j cij per unit cost of shipping from plant i to market i xij amount to ship between plant i and market j Then Minimize zij cij xij Such that i xij ai for all i i xijbj for all j plus non-negativity Let South Dakota S, Denver -D , New Jersey -N, California-C, Florida-F Minimize 2.5 SN+1.7 SC+ 1,8 SF + 2.5 DN+ 1.8 DC + 14 DF Subject to SN SC SF <350 DN+ DC+ DF <600 SNDN SC+ DC SF + DF >m 275 SN, SC, SF, DN, DC, DF>-0 >325 300 You are required to create a least cost shipping schedule between markets and plants. The markets are New Jersey, California, Florida and the plants are South Dakota, Denver. South Dakota only have 350 units available of supplies and Denver only have 600 units. The demand are only in New Jersey, California, Florida respectively 325, 300, 275 units. Now we inject into the model two locations, Pennsylvania and Ohio, where we have to send things first, and they are processed in some way, and then sent on to either New Jersey, California, or Florida. The cost to ship between markets and plants and is South Dakota to Pennsylvania is 1.2 South Dakota to Ohio is 0.9 Denver to Pennsylvania is 1.8 Denver to Ohio is 1.6 Pennsylvania to New Jersey is 0.7 Pennsylvania to California is 1.4 Pennsylvania to Florida is 1.5 Ohio to New Jersey is 0.9 Ohio to California is 0.4 Ohio to Florida is 1.4 how much you ship from South Dakota to Pennsylvania, how much you ship from South Dekota to Ohio, how much you ship from Denver to Pennsy Denver to Ohio, and then continuing on, how much you ship from Pennsytvania to New Jersey California to Florida, and then three more, how much you ship from Ohio to New Jersey, California, and Florida. So those are the decision variables. You just have the cost for each of those decision variables on a per unit basis, and you want to minimize the total cost. ia, how much you ship from