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Marc Hernandez's construction firm currently has three projects in progress. Each requires a specific supply of gravel. There are three gravel pits available to provide for Hernandez's needs, but shipping costs differ from location to location.
The following table summarizes the transportation cost. To From Job 1 Job 2 Job 3 Tonnage AllowanceCentral pit $9 $ 8 $ 7 3,000Rock pit $7 $11 $ 6 4,000Acme pit $4 $ 3 $12 6,000
Job requirements (tons) (Job1) 2,500 (Job 2) 3,750 (Job 3) 4,850 Problem A) Determine Hernandez's optimal shipping quantities so as to minimize total transportation costs. Problem B) It is the case that Rock Pit and Central Pit can send gravel by rail to Acme for $1 per ton. Once the gravel is relocated, it can be trucked to the jobs. Reformulate this problem to determine how shipping by rail could reduce the transportation costs for the gravel.
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