Consider Forbelt Corporation has a oneyear contract to supply motors for all refrigeratorsproduced by the Ice Age Corporation. Ice Agemanufactures the refrigerators at four locationsaround the country: Boston, Dallas, Los Angeles, and St. Paul. Plans callfor the following number (in thousands) of refrigerators to be produced ateach location:Boston 50Dallas 70Los Angeles 60St. Paul 80Forbelt’s three plants are capable of producing the motors. The plants andproduction capacities (in thousands) areDenver 100Atlanta 100Chicago 150Because of varying production and transportation costs, the profit thatForbelt earns on each lot of 1000 units depends on which plant producedthe lot and which destination it was shipped to. The following table givesthe accounting department estimates of the profit per unit (shipments willbe made in lots of 1000 units):Shipped toProduced at Boston Dallas Los Angeles St. PaulDenver 7 11 8 13Atlanta 20 17 12 10Chicago 8 18 13 16Consider the profit maximization problem of determining how many motorsshould be produced at each plant and how many motors should be shippedfrom each plant to each destination. a. Develop a network representation of the problem. b. Compute an optimum using a computer. What are optimal profits?