274
Rs./day, whereas about 180 Rs. is the minimum requirement to live in Purulia.
Overall, in destination regions, the average income is 1800 Rs/day. But the minimum requirement to live in a moderate way is Rs. 1200 per day. Average income
fluctuation between the source and destination regions is portrayed in Table 3.
Sometimes it is quite evitable that all the categories of laborers cannot meet the
basic requirement of money to live, so they are compelled to live in the slum areas
by creating “Jhupris,” a completely unhealthy unhygienic situation. Average
income/day between the destination regions are identified as the variables x 1, x 2 ,…
.,x 8, and with the help of the CPLEX model, estimation of the feasible solution of
wages is done. Workers always try to maximize their wages within the limited
working hours. So, we have to maximize the objective function as follows:
Maximize
x
x
x
x
x
x
x
x z
…
+
+
+
+
+
+
+
=
7
10
10
10
10
10
10
10
1
2
3
4
5
6
7
8
(15.6)
In subject to,
100
120
180
1
2
x
x
+
≥
(15.7)
500
900
1000
1200
1
5
8
x
x
x
+
+
≥
(15.8)
900
1300
1600
5
8
x
x
+
≥
(15.9)
1200
900
800
800
4
5
8
x
x
x
+
+
≥
(15.10)
500
1000
800
5
6
x
x
+
≥
(15.11)
900
1200
7
x ≥
(15.12)
900
1000
3
x ≥
(15.13)
The above seven equations have their lower, level and marginal values altogether.
The CPLEX model summary of variables gives the value of the objective function
as 70.444 means the overall model can be maximized up to 70.444 points. Estimating
the average income/day, the optimum point and feasible regions (Fig. 15.9) are estimated graphically. The model equations with respect to the demand of workers are
as follows:
Maximize obj x
x
z
..7
10
9
1 0
1
+
=
(15.14)
100
120
180
9
1 0
x
x
+
≥
(15.15)
1600
200
1200
9
1 0
x
x
+
≥
(15.16)
As it becomes a maximization problem, the feasible region is estimated as an
unbounded solution (ABCDE, Fig. 15.9). The optimum point B (75, 100) is obtained
S. Raha and S. K. Gayen