It is given that the satellites serving either B, C or S do not serve O.
From (1), let the number of satellites serving B, C and S be 2K, K, K respectively.
Let the number of satellites exclusively serving B be x.
From (3), the number of satellites exclusively serving C and exclusively serving S will each be 0.3x
From (4), the number of satellites serving
O is same as the number of satellites serving only
C and
S. Let that number be
y.
Since the number of satellites serving
C is same as the number of satellites serving
S, we can say that
(number of satellites serving only
B and
C)+0.3x+100+y=( number of satellites serving only
B and
S)+ 0.3x+100+y Let the number of satellites serving only
B and
C= the number of satellites serving only
B and
S =Z Therefore, the venn diagram will be as follows
Given that there are a total of 1600 satellites
⇒x+z+0.3x+z+100+y+0.3x+y=1600
1.6x+2y+2z=1500............(1)
Also
K=0.3x+z+y+100 Satellites serving
B=2K=x+2z+100 ⇒2(0.3x+z+y+100)=x+2z+100
0.4x=2y+100 x=5y+250....(2)
Substituting ( 2 ) in (1), we will get
1.6(5y+250)+2y+2z=1500 10y+2z=1100 Z=550−5y..........(3)
From
2, the number of satellites serving B exclusively is
x=5y+250 This is minimum when y is minimum.
Minimum value of
y=0 The minimum number of satellites serving
B exclusively
=5×0+250=250.