Consider the following transportation problem 1 2 3 Supply 1 5 3 7 54 2 5 11 6 86 3 10 5 2 77 4 5 4 13 123 Demand77 96 167 Is this a balanced or unbalanced transportation problem? [Type 1 for Yes; Type 2 for No:, Type 3 for "Not Applicable"] After the first iteration how many units are remaining to satisfy the demand at destination 1? [Use North West Corner method] How many units units are assigned to the second northwest corner cell (iteration 2)? How many units are assigned to the third northwest corner cell (iteration 3)? After iteration 3, what is the remaining demand for destination 2? After iteration 3, what is the remaining supply from source 2? After performing iteration 4 using the northwest corner cell method, what is the remaining supply for the the row (source) containing the cell that was just assigned? What is the total cost of transporting all the units allocated in the 5th iteration? Time left 0:29:33 How many units are assigned in the last iteration using the northwest corner cell method? What is the total cost of transportation using the northwest corner cell algorithm? Using the basic feasible solution obtained above, use the MODI method to check if you have an optimal solution. To start you off, label row 1, row 2, row 3 and row 4 and U1, U2, U3 and U4, respectively. Then label columns 1, 2 and 3 as V1, V2 and V3, respectively. Write down all the equations for NON-ALLOCATED cells according to the MODI technique. Let U2=0 and calculate the value of V1 What is the value of U1 What is the value of V2? What is the value of U3? What is the value of V3? What is the value of U4 What is the cell evaluation, D12 (for the unallocated cell in row 1 column 2)? [Cell evaluation refers to obtaining the cell's opportunity cost] What is the cell evaluation, D13 (for the unallocated cell in row 1 column 2)? What is the cell evaluation, D23 (for the unallocated cell in row 2 column 3)? What is the cell evaluation, D31 (for the unallocated cell in row 3 column 1)? What is the cell evaluation, D41 (for the unallocated cell in row 4 column 1)? What is the cell evaluation, D42 (for the unallocated cell in row 4 column 2)? Note: To check for optimality you continue as follows: From the cell containing the most negative value of the cell evaluations (Dij), draw a closed loop comprising of horizontal and vertical lines in such a way that the corner cells are occupied cells. From this cell assign + and - to the corner cells of your loop. Using this loop, write down the number of units to be redistributed to other destinations with an objective of minimizing the cost of transportation? Try finding the optimal solution during your free time- the optimal solution is not needed in this assignment. In which row is the cell evaluation with the most negative value