Reference no: EM133011759

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 Allowance
Central pit              $9                  $ 8              $ 7                       3,000
Rock pit                  $7                  $11             $ 6                        4,000
Acme 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.