0 A B C D E F G H 1 K L M N 1 Indiana Aggregates 2 In Tons Indiana Aggregates harvests sand from its pits, brings it to

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0 A B C D E F G H 1 K L M N 1 Indiana Aggregates 2 In Tons Indiana Aggregates Harvests Sand From Its Pits Brings It To 1 (120.86 KiB) Viewed 52 times

0 A B C D E F G H 1 K L M N 1 Indiana Aggregates 2 In Tons Indiana Aggregates harvests sand from its pits, brings it to a depot for mixing, and then sends the sand to 3 Pit Information Prodn Cost Capacity its customers to make concrete. The sand contains impurities that affect the quality of the concrete, and 4 Pit 1 $15 200 thus it is mixed to ensure that these impurities are kept to an acceptable level. 5 Pit 2 $18 140 6 Pit 3 $22 200 7 8 Cost to Ship From Depot to Customer (per Ton) The accompany tables give us the following information: 9 Customer 1 Customer 2 Customer 3 Customer 4 • The cost per ton to harvest the sand at each pit, 10 Depot $42 $59 $75 $112 The harvest maximum capacity in tons for each pit, 11 Demand (Tons) 150 120 100 100 The amount of silt and mica contained in the sand from each pit, • The demand from each customer in tons which must be met, 12 • The cost to ship per ton from each pit to the depot, and 13 Cost to Ship From Pit to Depot (per Ton) • The cost to ship per ton from the depot to each customer. 14 Pit 1 $ 30.0 15 Pit 2 $ 50.0 To meet the maximum allowed impurities, the sand is mixed. It is assumed that the 16 Pit 3 $ 20.0 resulting mix is a result of a weighted average of the inputs. For instance, if 1 ton of 17 sand with 8% silt is mixed with 3 tons of sand with 4% silt, the result is 4 tons of sand with 5% silt. 18 Impurities Silt Mica 19 Pit 1 8.5% 6.0% Use a linear program to find the amount of sand to bring to the depot from each pit, as 20 Pit 2 6.0% 4.5% well as the amount of product to ship to each customer from the depot such that the 21 Pit 3 5.0% 3.0% 22 23 The maximum allowed % of silt and mica impurities) in the sand going 24 to customers, is 6.5% for silt and 4.5% for Mica. 25 26 27 28 29 30