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 costs:

(a) Determine Hernandez€™s optimal shipping quantities so as to minimize total transportation costs.
(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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TO TONNAGE FROM Central pit Rock pit Acme pit Job requirements JOB1 JOB2 JOB 3 ALLOWANCE $9 $7 $4 $3 : $7 3,000 3a 56 4,000 4.000 2,500 3,750 4,850 (tons)