5. A warehouse manager needs to determine the amounts of goods to be sent to three retailers from the three warehouses of the company. Warehouse 1 has a supply of 40 units, Warehouse 2 has 50 units, and Warehouse 3 has 60 units. The demand consists of 50 units for Retailer 1, 70 units for retailer 2, and 30 units for Retailer 3. Given the transportation costs in the table, construct the transportation tableau to minimize the total cost of sending goods from warehouses to retailers. Warehouse 1 Warehouse 2 Warehouse 3 Retailer 1 $17 $14 $12 Retailer 2 $15 $13 $14 Retailer 3 $18 $19 $16 (a) Find a basic feasible solution using the northwest-corner rule and starting with this solution, apply the transportation simplex method to find an optimal solution. (b) Find a basic feasible solution using the minimum-cost rule and starting with this solution, apply the transportation simplex method to find an optimal solution. (c) Find a basic feasible solution using the Vogel's method and starting with this solution, apply the transportation simplex method to find an optimal solution. (d) Compare the number of iterations required in (a)-(c).

5. A warehouse manager needs to determine the amounts of goods to be sent to three retailers from the three warchouses of the company. Warehouse 1 has a supply of 40 units, Warchouse 2 has 50 units, and Warchouse 3 has 60 units. The demand consists of 50 units for Retailer 1,70 units for retailer 2 , and 30 units for Retailer 3 . Given the transportation costs in the table, construct the transportation tableau to minimize the total cost of sending goods from warchouses to retailers. (a) Find a basic feasible solution using the northwest-corner rule and starting with this solution, apply the transportation simplex method to find an optimal solution. (b) Find a basic feasible solution using the minimum-cost rule and starting with this solution, apply the transportation simplex method to find an optimal solution. (c) Find a basic feasible solution using the Vogel's method and starting with this solution, apply the transportation simplex method to find an optimal solution. (d) Compare the number of iterations required in (a)-(c)