[10 points] Capacitated plant location problem: WSU4330 is a manufacturing consulting firm and has been tasked with determining the locations of its plants. WSU4330's customers are located in the 16 states shown in the table below, and there are four potential plant location sites (Los Angeles, Tulsa, Denver, and Seattle). The fixed cost of opening an office in Los Angeles is $155,000; $134,000 in Tulsa; $140,000 in Denver; and $165,000 in Seattle. The number of trips to each customer and the travel costs are shown in the table below; also, each truck at each plant is expected to take a max of 20 trips each year. If a max of 10 trucks are at each office (develop a mathematical optimization model and use excel to determine the optimal capacitated plant location) a. Where will the plants be located? b. How many trips are needed from each plant? c. What is the distance based objective function value? State #Trips 200 40 35 Seattle 150 150 300 300 150 100 25 20 25 75 125 25 25 LA 75 150 150 150 100 75 150 150 175 150 300 125 250 250 300 250 Washington Oregon California Idaho Nevada Montana Wyoming Utah Arizona Colorado New Mexico North Dakota South Dakota Nebraska Kansas Oklahoma Travel Costs Tulsa Denver 25 75 200 200 150 200 125 200 175 175 100 150 100 200 100 125 125 125 125 200 175 125 100 250 75 250 125 250 200 30 25 250 65 40 150 30 250 300 200 200 250 300 300 125 10 30 40 55 [10 points] Capacitated plant location problem: WSU4330 is a manufacturing consulting firm and has been tasked with determining the locations of its plants. WSU4330's customers are located in the 16 states shown in the table below, and there are four potential plant location sites (Los Angeles, Tulsa, Denver, and Seattle). The fixed cost of opening an office in Los Angeles is $155,000; $134,000 in Tulsa; $140,000 in Denver; and $165,000 in Seattle. The number of trips to each customer and the travel costs are shown in the table below; also, each truck at each plant is expected to take a max of 20 trips each year. If a max of 10 trucks are at each office (develop a mathematical optimization model and use excel to determine the optimal capacitated plant location) a. Where will the plants be located? b. How many trips are needed from each plant? c. What is the distance based objective function value? State #Trips 200 40 35 Seattle 150 150 300 300 150 100 25 20 25 75 125 25 25 LA 75 150 150 150 100 75 150 150 175 150 300 125 250 250 300 250 Washington Oregon California Idaho Nevada Montana Wyoming Utah Arizona Colorado New Mexico North Dakota South Dakota Nebraska Kansas Oklahoma Travel Costs Tulsa Denver 25 75 200 200 150 200 125 200 175 175 100 150 100 200 100 125 125 125 125 200 175 125 100 250 75 250 125 250 200 30 25 250 65 40 150 30 250 300 200 200 250 300 300 125 10 30 40 55
