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 cost differ from location to location. The following table summarize the transportation costs (per ton):
|
To:
|
|
From
|
Job 1
|
Job 2
|
Job 3
|
|
Central pit
|
$9
|
$8
|
$7
|
|
Rock pit
|
$7
|
$11
|
$6
|
|
Acme pit
|
$4
|
$3
|
$2
|
The job requirements (tons) for the three jobs are 2500, 3750, and 4850, respectively. The tonnage allowance at the three pits are 3000, 4000, and 6000 tons for Central, Rock and Acme, respectively. Hernandez's optimization problem is to find the optimal shipping quantities so as to minimize total transportation costs. Formulate the problem and solve it using Solver. Report the minimum transportation cost.
Set up LP models (decision variables, objective function, and constraints) first. Then solve using a spreadsheet model.
Determine Hernandez's optimal shipping quantities so as to minimize total transportation costs.