Problem:
Forbelt Corporation: Transportation problem
Forbelt Corporation has a one-year contract to supply motors for all refrigerators produced by the IAC. ICA manufacures he refrigerators at 4 locations around the country: Boston, Dallas, Los Angeles and St. Paul. Plans call for the following number ( in thousands) of refrigerators to be produced at each location:
Boston--50
Dallas ---70
Los Angeles--60
St. Paul---80
Forbelt's three plants are capable of producing the motors. Th plants and production capacities (in thousands) are;
Denver 100
Atlanta 100
Chicago 150
Because of varying production and transportation costs, the profit that Forbelt earns on each lot of 100 unites depends on which plant produce the lot and which destination it was shpped to. The following table gives the accounting department estimate of the profit per unit ( shipments will be made in lots of 1000 units)
Shipped to
Produced at ---- Boston ---- Dallas---Los Angeles---St. Paul
Denver-------------7-----------11----------8---------------13---
Atlanta------------20----------17----------12--------------10
Chicago------------8-----------18----------13--------------16--
With profit maximization as a criterion, Forbelts management wants to determinate how many motors should be produced at each plant and how many motors should be shipped from each plant to each destination.
a. Develop a network representation of this problem.
b. Find the optimal solution