Study the problem shown in the notes titled "Balanced Transportation Problem-Textbook Example". Now look at the spreadsheet shown on page 2 of the notes. Show the mathematical expression of the value shown in cell B63 in terms of the decision variables. Example in Section 10.1 The transportation problem is balanced because the total supply = total demand Total supply = 5000 + 6000 + 2500 = 13500 units Total demand = 6000 + 4000 + 2000 + 1500 = 13500 units Decision variables: Xij = number of units shipped from plant i to distribution center i where i = 1, 2, and 3 and j = 1, 2, 3, and 4. Following Figure 10.1, plant 1 is located in Cleveland, plant 2 is located in Bedford, and plant 3 is located in York. Similarly, distribution center 1 is located in Boston, etc. There are 12 (or 3*4) decision variables because there are 12 distribution routes (arcs). Objective function: Minimize the total transportation cost where the total transportation cost = (3)X11 + (2)x12 + .....+ (4)X33+ (5)X34 Supply constraints: The total number of units sent from Cleveland plant must be less than or equal to the plant capacity in Cleveland. Thus, X11+X12 + X13 + X14 = 0; i = 1, 2, 3; j = 1, 2, 3, 4. G H A A B C D E 48 49 The unit transportation costs ($/u) 50 To distribution centers 51 From plant Boston Chicago St. Louis Lexington 52 Cleveland 3 2 7 6 53 Bedford 7 5 2 54 York 2 5 4 uw 57 Units sent in each route: 58 To distribution centers 59 From plant Boston Chicago St. Louis Lexington 60 Cleveland 2 T 61 Bedford 62 York 5000 6000 2500 13500 6000 4000 2000 1500 13500