(Recovery for each type of raw material*Corresponding weight of raw material to be
ordered per batch)
£
4,000 Kgs per batch (or 4 Tons per batch)
\
(0.84*T + 0.74*R + 0.85*S + 0.94*L + 0.97*I + 0.25*H + 0.95*P)
£
4 Tons (per batch) * B
\
(0.84*T + 0.74*R + 0.85*S + 0.94*L + 0.97*I + 0.25*H + 0.95*P) – 4B
£
0
(b)
Constraint on the minimum quantity (in Tons) of raw material per batch

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Minimum quantity (in tons) of Tasla, Rangeen, Imported Scrap and High Carbon that can be
used in a batch is 0%
\
(T / T
RMT
)*100
³
0;
\
(R / T
RMT
)*100
³
0;
\
(I / T
RMT
)*100
³
0;
\
(H / T
RMT
)*100
³
0
\
T
³
0
[Min Tasla constraint]
R
³
0
[Min Rangeen constraint]
I
³
0
[Min Imported Scrap constraint]
H
³
0
[Min High Carbon constraint]
Minimum quantity of Sponge that can be used in a batch is 10%
\
(S / T
RMT
)*100
³
10
\
9*S – (T + R + L + I + H + P)
³
0
[Min Sponge constraint]
Minimum quantity of Local Scrap that can be used in a batch is 15%
\
(L / T
RMT
)*100
³
15
\
17*L – 3*(T + R + S + I + H + P)
³
0
[Min Local Scrap constraint]
Minimum quantity of Pig Iron that can be used in a batch is 5%
\
(PI / T
RM
)*100
³
5
\
19*P – (T + R + S + I + H + L)
³
0
[Min Pig Iron constraint]
(c)
Constraint on the maximum quantity (in Tons) of raw material per batch
Maximum quantity of Tasla that can be used in a batch is 50%
\
(T / T
RMT
)*100
£
50
\
-T + R + S + L + I + H + P
³
0
[Max Tasla constraint]
Similarly for the other raw materials,
(R / T
RMT
)*100
£
25
\
-3*R + T + S + L + I + H + P
³
0
[Max Rangeen constraint]
(S / T
RMT
)*100
£
50
\
T + R - S + L + I + H + P
³
0
[Max Sponge constraint]
(L / T
RMT
)*100
£
80
\
-L + 4*(T + R + S + I + H + P)
³
0
[Max Local Scrap constraint]
(I / T
RMT
)*100
£
80
\
-I + 4*(T + R + S + L + H + P)
³
0
[Max Imported Scrap constraint]
(H / T
RMT
)*100
£
20
\
-4*H + T + R + S + L + I + P
³
0
[Max High Carbon constraint]
(P / T
RMT
)*100
£
10
\
-9*P + T + R + S + L + I + H
³
0
[Max Pig Iron constraint]
(d)
Constraint on the total time (in hours) for production in a month
Time for production in a month
= [0.2 + (0.3 * Total Raw material weight in tons per batch/B)] * B
£
600 Hrs
= 0.3 (T + R + S + L + I + H + P) + 0.2 B +
£
600
(e)
Constraint on the Maximum Availability of Raw Material During the Following Month
We assume that the quantity of raw material available in the following month to produce
requisite finished product that would optimise profit would be much lesser than the maximum
available quantity of the raw materials. Therefore, presently, the maximum availability of raw
material during the following month is not being considered as constraint while optimising the
profit for a batch production.
(f)
Un-constrained Variables

Weights of all raw materials would be
³
0 and also the number of batches produced in a month
would be
³
0
\
T
³
0, R
³
0, S
³
0, L
³
0, I
³
0, H
³
0, P
³
0 & B
³
0
The LP Model thus obtained has been solved by Simplex LP method using the Excel Solver.
Based on the solution of the solver, following are calculated:-
Raw
Material
Rate/Ton
(INR)
Recovery
Min per
Batch
(% of
Raw
Material)
Max per
Batch
(% of
Raw
Material)
Max
per
Month
(Ton)
Weight
of
Raw
Materials
(in Tons)
per Month
Cost (INR) of
Raw Materials
for a Month
Weight of
Steel
Produced
(in tons) per
Month
Tasla
17,000
0.84
0%
50%
800
789.88
13427923.65
663.4974036
Rangeen
13,600
0.74
0%
25%
500
438.82
5967966.06
324.7275653
Sponge
17,800
0.85
10%
50%
1,000
175.53
3124405.76
149.1991516
Local
Scrap
20,000
0.94
15%
80%
1,000
263.29
5265852.41
247.4950633
Imported
Scrap
23,000
0.97
0%
80%
1,500
0.00
0.00
0
HC
2,500
0.25
20%
300
0.00
0.00
0
Total
1755.28
29576537.70
1468.30
Cost of Electricity
per Month =
7177506.034

- Fall '19