Forbelt Corporation has a 1-year contract to supply motors for all refrigerators produced by the Ice Age Corporation. Ice Age manufactures the refrigerators at the four 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 has three plants that are capable of producing the motors. The plants and productions capacities (in thousands) 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 produced the lot and which destination it was shipped to. The following table fives the accounting department estimates of the profit per lot (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, Forbelt wants to determine how many motors should be produced at each plant and how many motors should be shipped from each plant to each destination. a- Write a linear programming formulation of this problem. b- Find the optimal solution by using Excel. Include the computer output. c- Prepare a report using PowerPoint. The report should include: - Introduction to the problem -Decisions to be made -Formulation -Solution Method (Linear programming using SOLVER) -Solution: overall cost, how many motors should be produced at each plant and how many motors should be shipped from each plant to each destination