Consider the following transportation problem, with four source nodes (1,2,3,4) and two destination nodes (A,B), represented in the following network diagram. Supply capacities at the source nodes are 100, 200, 150, 50 respectively; demand quantity at each destination is 250; and the cost of transportation via the arcs from each source node to the two destinations A and B (indicated in parentheses) are Node1 to A,B (5, 6), Node2 to A,B (4, 2), Node3 to A,B (3,6), Node4 to A,B (9,7). All these details are indicated in the diagram.

Instructions: Clearly indicate the answers to the questions here itself wherever possible. (Indeed, you may upload, if you prefer, a scanned or photo of your hand-written formulation, and an Excel file for showing supporting work in the file-upload questions towards the end. Prefix the file name with your last name and question number.)

a) Write the LP formulation that minimizes the transportation cost clearly marking the decision variables, objective function and constraints.

b) Solve the problem using Excel solver and answer the questions below.

(i) What is the value of the objective function, i.e., minimized cost of Transportation?

(ii) Indicate the Optimal Solution, i.e., quantities transported in each arc.

5 100 1 6 A 250 4 200 2 2 3 B 250 150 3 6 9 50 4 7