please write solve and explain detail at d) stepping stone method

2. [25 pts.] 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 ) 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.] 3. [25 pts.] Four projects are available for investment. The projects require the cash flows and yield the net present values (NPV) (in millions) shown in the following table. If 20 million Lira is available for investment at time 0 , find the investment plan that maximizes NPV. All investments are required to be 0 or 1 (fractional investment values are not permitted). a. Formulate the mathematical model. (Write the decision variables, objective function and the constraints.) [10 pts.] b. Find the optimal solution by using Branch and Bound method (Draw the branch and bound tree clearly, write also lower bounds (LB) ) (Left branches xi=0, right branches xi=1 ) [15 pts. ]