[Marks: 4+8+3=15] Question#03: a) Let a i is the total quantity of product available at origin i (i= 1,2, .....,m) and b j is the total product required at destination j (j= 1,2,...,n). Let x ij is the units shipped per route from source I to destination j and c ij is the cost of shipping one unit from source I to destination j for each route. For this given problem construct a standard form of linear programming problem and show it graphically. b) A company has factories at F1, F2 and F3 which supply warehouses at W1, W2 and W3. Weekly factory capacities are 200, 160 and 90 units respectively. Weekly warehouse requirements are 180, 120 and 150 units respectively. Units shipping costs (in Tk.) are as follows: Warehouse W1 W2 W3 Supply F1 16 20 12 200 Factory F2 14 8 18 160 F3 26 24 16 90 Demand 180 120 150 450 Find the minimum transportation cost using Least Cost method and Vogel's approximation method. [Marks: 7+8=15]