A tin box company has four factories that supply to 5 warehouses. The variable cost of manufacturing and shipment of one ton of product from each factory to each warehouse are shown in the matrix given below, Factory capacities and warehouse requirements are shown in the margin. After several iterations the solution obtained is also shown. Factories W X Y Z Req Warehouses (Cost in Rs. per unit) BC DE A 10 30 40 17 13 6 9 14 25 6 20 17 15 20 11 15 10 20 50 30 11 9 12 11 14 10 30 14 12 12 6 40 40 DMY 20 (a) Is this an optimal solution? How do you know? (b) Is there an alternate solution? If so find it. 0 0 0 0 20 Capacity 75 45 30 50 200 (c) Suppose some new equipment was installed that reduces the variable operation cost by Rs. 2/- per ton in factory X, is the shipping schedule remain optimum? If not what is the new optimum? (d) Suppose the freight charges from W to A were reduced by Rs.2/- would this change the shipping schedule? If so what is the new optimum? (e) How much would the manufacturing cost have to be reduced in W before production would be increased beyond 55 tons?