Consider the following transportation table for a minimization problem. For Y$,$ substitute your student numbers last digit and calculate the unit transportation cost of factory to warehouse for the given table. $($For example: If your student number last digit is $1,$ unit transportation cost of factory $1$ to warehouse $1$ is $8+1=9)$ Warehouse $1$Warehouse $2$Warehouse $3$SupplyFactory $18$TL$+$Y$20$TL$+$Y$11$TL$+$Y$100$Factory $219$TL$+$Y$15$TL$+$Y$21$TL$+$Y$60$Factory $322$TL$+$Y$12$TL$+$Y$26$TL$+$Y$40$Demand$508070$ a$.$ 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$)[10$ pts$.]$