3. (30 points) Consider the transportation table below. Factory 4 3 1 $2 Warehouse 2 EP $4 3 $4 4 $1 150 Supply 10 3 7 7 200 6 50 100 7 20 5 150 50 150 200 500 500 Demand a. Define the decision variables b. Write a linear programming model for this problem. ICE c. Use the Northwest-Comer Method, the Least-Cost Method and the VAM to get the starting feasible solution. d. Find the optimal solution using the transportation algorithm discussed in class by considering the least optimal of the objective function computed in (c). e. Formulate a network model to illustrate the optimal solution.