RICE TRANSPORTATION PROBLEM There are five silos (suppliers) coded as A, B, C, D and E...

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RICE TRANSPORTATION PROBLEM There are five silos (suppliers) coded as A, B, C, D and E in Louisiana supplying rice regularly to buyers in four major cities of Louisiana. The related data has been collected from the concerned suppliers for the purpose of a mathematical formulation of the transportation problem. The transportation cost of different suppliers to the same destination varies to some extent due to their own policies and distances. Transportation costs per ton of rice from suppliers to destinations (Shreveport, Alexandria, Lake Charles and Lafayette) are displayed in Table 1. Table 1: Transportation cost (S/Ton). Suppliers B C D ABCD E E Shreveport (W) 50 60 65 75 150 Table 2: Available quantity (Tons) Supplier Quantity Available (Tons) A 4000 5000 Destination Alexandria Lake Charles (X) 100 4500 4000 5000 110 130 105 125 (Y) 85 65 75 75 95 Table 2 shows the quantity available at these suppliers and Table 3 shows the total demand by the buyers from these suppliers during a year. Lafayette (Z) 150 155 80 Destination Shreveport (W) Alexandria (X) Lake Charles (Y) Lafayette (Z) 160 125 Table 3: Total demand at different destinations Demand (Tons) 6500 3000 8000 5000 The objective of this transportation problem is to find the optimum quantities of rice supply from each supplier to each buyer's destination to minimize the total cost of transportation. The demand at each destination has to be satisfied by not exceeding the available quantity from any supplier. 1. Formulation and LP solution: Q1. (a) Formulate the above problem as a linear programming (LP) problem and solve it by computer with any LP-solver (Such as, MATLAB or Excel Solver). (b) Show your efforts with (a) the codes you write in the LP-solver or a screen shot of the solver and (b) the output from the solver. (c) Highlight/circle your answers (solution of the variables and objective functional values) RICE TRANSPORTATION PROBLEM There are five silos (suppliers) coded as A, B, C, D and E in Louisiana supplying rice regularly to buyers in four major cities of Louisiana. The related data has been collected from the concerned suppliers for the purpose of a mathematical formulation of the transportation problem. The transportation cost of different suppliers to the same destination varies to some extent due to their own policies and distances. Transportation costs per ton of rice from suppliers to destinations (Shreveport, Alexandria, Lake Charles and Lafayette) are displayed in Table 1. Table 1: Transportation cost (S/Ton). Suppliers B C D ABCD E E Shreveport (W) 50 60 65 75 150 Table 2: Available quantity (Tons) Supplier Quantity Available (Tons) A 4000 5000 Destination Alexandria Lake Charles (X) 100 4500 4000 5000 110 130 105 125 (Y) 85 65 75 75 95 Table 2 shows the quantity available at these suppliers and Table 3 shows the total demand by the buyers from these suppliers during a year. Lafayette (Z) 150 155 80 Destination Shreveport (W) Alexandria (X) Lake Charles (Y) Lafayette (Z) 160 125 Table 3: Total demand at different destinations Demand (Tons) 6500 3000 8000 5000 The objective of this transportation problem is to find the optimum quantities of rice supply from each supplier to each buyer's destination to minimize the total cost of transportation. The demand at each destination has to be satisfied by not exceeding the available quantity from any supplier. 1. Formulation and LP solution: Q1. (a) Formulate the above problem as a linear programming (LP) problem and solve it by computer with any LP-solver (Such as, MATLAB or Excel Solver). (b) Show your efforts with (a) the codes you write in the LP-solver or a screen shot of the solver and (b) the output from the solver. (c) Highlight/circle your answers (solution of the variables and objective functional values)