• A manufacturing firm produces diesel engines in four cities—Phoenix, Seattle, St. Louis, andDetroit. The company is able to produce the following numbers of engines per month: Plant Production 1. Phoenix 5 2. Seattle 25 3. St. Louis 20 4. Detroit 25 Three trucking firms purchase the following numbers of engines for their plants in three cities: Firm Demand A. Greensboro 10 B. Charlotte 20 C. Louisville 15 The transportation costs per engine (in hundreds of dollars) from sources to destinations are shown in the following table from A B C 1 7 8 5 2 6 10 6 3 10 4 5 4 3 9 11 However, the Charlotte firm will not accept engines made in Seattle, and the Louisville firm will not accept engines from Detroit; therefore, those routes are prohibited Formulate this problem as a linear programming model.