need help with this problem please
Forbelt Corporation has one year contract to supply motors for all refrigerators produce by the Ice Age Corporation. Ice Age manufactures the refrigerators at four locations around the country. Boston, Dallas, Los Angeles, and St Paul. Plants call for the following number (in thousand) of refrigerators to be produce at each location.
Boston 50 Dallas 70 Los Angeles 60 St Paul 80
Forbeltâ€™s three plants are capable of producing the motors. The plants and production capacities are
Denver 100 Atlanta 100 Chicago 150
Because of varying production and transportation cost, the profit that Forbelt earns on each lot of 1000 units depends on which plant produce the lot and which destination it was shipped to. The following table gives the accounting department estimates of the profit per unit (shipments will be made in 1000)
Produce 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. Forbeltâ€™s management wants to determine how many motors should be produce 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.