Problem 2. (40 points] New Belgium Beer Co. out of Colorado will begin providing beer to the states of Georgia (GA), North Carolina (NC) and South Carolina (SC). The demand for beer in GA, NC, and SC is 4000, 3000, 3000 barrels, respectively. New Belgium produces beer in a factory in Colorado (CO), then sends it to a warehouse in either Tennessee (TN) which can handle up to 3500 barrels a year, or Illinois (IL) which can handle up to 7500 barrels a year. The warehouses in TN and IL proceed to send the beer to GA, NC, SC. New Belgium cannot send beer directly from Colorado to GA, NC or SC. New Belgium's factory in Colorado (CO) supplies 10,000 barrels of beer each year. Tennessee and Illinois do not demand any beer, but they can ship beer to GA, NC, or SC at the cost per barrel given below. From/to GA NC IN $100 $250 $350 $450 SC $150 $350 IL The cost to send beer from Colorado to Tennessee and Colorado to Illinois is $200 and $300 per barrel, respectively. The cost to send beer from Colorado to Tennessee and Colorado to Illinois is $200 and $300 per barrel, respectively. (a) (10 points) Use a network representation that models the problem as a balanced minimum cost network flow problem. Label all nodes, and specify the lower and upper bounds and costs of all arcs, as well as the net supplies of all nodes. (b) (15 points) Formulate the problem as a linear program following the network representation in part (1) (c) (5 points) Suppose New Belgium began producing 12,000 barrels of beer instead of 10,000 barrels of beer. Luckily, they can ship excess beer to Wisconsin, who has volunteered to absorb any extra supply that New Belgium has. The beer should be shipped directly from Colorado to Wisconsin at a cost of $600 per barrel. How would you modify your network from (a)? (d) (10 points) New Belgium must purchase a license if they send more than 3000 barrels of beer from Tennessee to Georgia. Write an integer programming constraint that states that if they send more than 3000 barrels from TN TO GA, then a licence must be purchased. You may use the same decision variable defined earlier, and/or introduce new one if you deem necessary. Problem 2. (40 points] New Belgium Beer Co. out of Colorado will begin providing beer to the states of Georgia (GA), North Carolina (NC) and South Carolina (SC). The demand for beer in GA, NC, and SC is 4000, 3000, 3000 barrels, respectively. New Belgium produces beer in a factory in Colorado (CO), then sends it to a warehouse in either Tennessee (TN) which can handle up to 3500 barrels a year, or Illinois (IL) which can handle up to 7500 barrels a year. The warehouses in TN and IL proceed to send the beer to GA, NC, SC. New Belgium cannot send beer directly from Colorado to GA, NC or SC. New Belgium's factory in Colorado (CO) supplies 10,000 barrels of beer each year. Tennessee and Illinois do not demand any beer, but they can ship beer to GA, NC, or SC at the cost per barrel given below. From/to GA NC IN $100 $250 $350 $450 SC $150 $350 IL The cost to send beer from Colorado to Tennessee and Colorado to Illinois is $200 and $300 per barrel, respectively. The cost to send beer from Colorado to Tennessee and Colorado to Illinois is $200 and $300 per barrel, respectively. (a) (10 points) Use a network representation that models the problem as a balanced minimum cost network flow problem. Label all nodes, and specify the lower and upper bounds and costs of all arcs, as well as the net supplies of all nodes. (b) (15 points) Formulate the problem as a linear program following the network representation in part (1) (c) (5 points) Suppose New Belgium began producing 12,000 barrels of beer instead of 10,000 barrels of beer. Luckily, they can ship excess beer to Wisconsin, who has volunteered to absorb any extra supply that New Belgium has. The beer should be shipped directly from Colorado to Wisconsin at a cost of $600 per barrel. How would you modify your network from (a)? (d) (10 points) New Belgium must purchase a license if they send more than 3000 barrels of beer from Tennessee to Georgia. Write an integer programming constraint that states that if they send more than 3000 barrels from TN TO GA, then a licence must be purchased. You may use the same decision variable defined earlier, and/or introduce new one if you deem necessary
