Draw the network diagram. $($Write the related parameters on nodes and arcs$)[4$ pts$.]$

b$.$ Formulate the linear programming model to minimize the total transportation cost. $($Write the decision variables, objective function and the constraints.$)[6$ pts$.]$

c$.$ Find a basic feasible solution for the given transportation problem using northwest corner method. Write the basic variables and their values clearly. $[5$ pts$.]$

d$.$ Find optimal solution by using stepping$-$stone method and the initial basic feasible solution you find in the previous question c$.($For each iteration: Calculate improvement indices, write loops and total cost