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 iteration the solution obtained is shown below.
|
Factories
|
A
|
B
|
C
|
D
|
E
|
DUMMY
|
SUPPLY
|
|
W
|
17
|
9
|
14
15
|
10
30
|
14
|
0
20
|
75
|
|
X
|
10
13
|
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 schedule remain optimum? If you what is the new optimum?
(d) Suppose the fright charges from W to A were reduced by two birr would this change the shipping schedule? If so what is the new optimum?
(e) How match would the manufacturing cost have to be reduced in W before production would be increased beyond 55 tons?