A tin box company has four factorial that supply to 5 ware house. 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 ware house requirement are shown in the margin. After several iterations the solution obtained also shown.
|
Factories
|
A
|
B
|
C
|
D
|
E
|
DUMMY
|
SUPPLY
|
|
W
|
17
|
9
|
14
25
|
10
30
|
14
|
0
20
|
75
|
|
X
|
13
10
|
6
20
|
11
15
|
11
|
12
|
0
|
45
|
|
Y
|
6
30
|
17
|
9
|
12
|
12
|
0
|
30
|
|
Z
|
15
|
20
|
11
|
14
|
6
|
0
|
50
|
|
Demand
|
40
|
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 two birr per ton in factory X, is the shipping schedules remain optimum? If not what is the new optimum?
(d) Suppose the freight charges from W to A were reduced by two birr would this change the shipping schedule? If so what is the new optimum?