Question

13. 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. Warehouses (Cost in Rs. per unit) A A B C D E Factories DMY Capacity 179 14 0 75 14 25 11 15 9 10 30 11 6 20 6 171 12 12 15 2011 20 14 10 Red 20 50 30 1 20 (a) Is this an optimal solution? How do you know? (b) Is there an alternate solution? If so find it. (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?

Answer 1

Answer:

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. Warehouses (Cost in Rs. per unit) A IDE Factories DMY Capacity 14 0 75 14 25 10 30 13 11 6 11 2015 10 6 17 9 12 30 15 2011 14 Req | 20 | 50 30 40 20 200 (a) Is this an optimal solution? How do you know? (b) Is there an alternate solution? If so find it. (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

0 10 | 911410 14 2015 30 10 151 201 11 14 46 o uxholm xul Let, xij reforesent amount of soroduct (in fon). shipping from its ractoris to jili warehouse Isis 4; 15; £ 6. Неи Co. [nitial В.Г. 2,8 = 25, 214 = 30, XVw=llo 201=10, 222 = 20 123 015, 131 30 = 10, nus 40. Here no. of allocation is = 9 - (m +1-1).

0 * 25 -20 30 *2091410 20 0 57 +20 120 01 6 17 0 12 12 401 5 o 10) 25. © © 6 199 12120 Here 15201 14 6 0 Vi 16 9 14 10 Here all 4;'>0, So a favnít vo So 6 12 – 20 B 25, 24 – 30 KUR | World 21 – 10 123 -35, 231-30 143= 10, nus40. 5. SON
d) note that initial BFS remains the same but in this case ∆(1,1)< 0.so check it. For checking here consider a loop form by cell (1,1),(1,3),(2,1) and (2,3).then just calculate the table as above.you seen that the next table gives the optimal solution.and solution will be x11=10,x13=15,x14=30,x22=20,x23=25,x31=30,x43=10,x45=40. And min cost just cost multiplied by corresponding amount x's and take their sum