Question

A gym club charges its members ₹300 per year. They get 1000 members. Now, for each ₹2 increase in the revenue (charge) , the club can expect to loose 5 members. How much should the gym charge per person to maximize its revenue? What will be the gym 's maximum revenue?

ANSWER WITH FULL CLARIFICATION...​

Answer 1

Explanation:
Gym charge is
C
=
$
300
and number of members are
M
=
1000
Revenue is
R
=
C
⋅
M
=
$
300000
. Let the number of
$
2
increase be
x
then revenue is
R
=
(
300
+
2
x
)
⋅
(
1000
−
5
x
)
R
=
−
10
x
2
+
2000
x
−
1500
x
+
300000
or
R
=
−
10
x
2
+
500
x
+
300000
or
R
=
−
10
(
x
2
−
50
x
)
+
300000
or
R
=
−
10
(
x
2
−
50
x
+
625
)
+
6250
+
300000
or
R
=
−
10
(
x
−
25
)
2
+
306250
;
R
will be maximum
when
x
−
25
=
0
∴
x
=
25
∴
2
x
=
50
;
C
=
300
+
50
=
350
;
M
=
1000
−
5
⋅
25
=
875
,
R
=
306250
and so gym charge
should be
$
350
from
875
members to get maximum
revenue or
$
306250
[Ans]