In the state of Bihar, in a particular region there are 5 coal mines which produce the following output at the indicated production costs:
|
Mine
|
Output
m.tons /day
|
Production Cost units
of 100 Rs. per metric ton
|
|
1
|
120
|
25
|
|
2
|
150
|
29
|
|
3
|
80
|
34
|
|
4
|
160
|
26
|
|
5
|
140
|
28
|
Before the coal can be sold to the steel making units, it must be cleaned and graded at one of the 3 coal preparation plants. The capacities and operating cost of these 3 plants are as follows.
|
Plants
|
Capacity
metric tons/day
|
Operating cost units of 100 Rs. per metric ton
|
|
A
|
300
|
2
|
|
B
|
200
|
3
|
|
C
|
200
|
3
|
All coal is transported by rail at a cost of Rs. 50 per metric ton kilometer and the distance in kilometers from each mine in the preparation plants are indicated below:
|
Preparation
Plant
|
Distance(in Km) to Mines
|
|
1
|
2
|
3
|
4
|
5
|
|
A
|
22
|
44
|
26
|
52
|
24
|
|
B
|
18
|
16
|
24
|
42
|
48
|
|
C
|
44
|
32
|
16
|
16
|
22
|
(i) Using a transportation model, determine how the output of each mine should be allocated to the three preparation plants to optimize cost.
(ii) Are alternative approaches possible? If so, what is the logic of lst allocation in these alternatives?
(iii) What is degeneration and when can it happen?