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

Forbelt’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)

  Shipped to  

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. Forbelt’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.