Question

A health club currently charges its 1500 members monthly membership dues of $41. The board decides to increase the amount of dues charged. The marketing dept. shows that each increase of $4 will result in the loss of 4 clients. How much should the club charge to optimize the revenue from monthly dues?

Answer 1

Oops, each increase of $1 will result in the loss of 4 members

Answer 2

this is approximately the same as the other one.

Answer 3

did you attempt this at all?

Answer 4

I got $51.25 but it says that isn't right

Answer 5

lets see. they will make
\[(41+x)(1500-4x)\] yes. where x is the dollar increase

Answer 6

otherwise known as
\[-4 x^2+1336 x+61500\]

Answer 7

a parabola facing down, max is at vertex, compute
\[\frac{-b}{2a}\] to get your answer

Answer 8

\[\frac{1336}{8}\] dang i get $167 maybe i made a mistake

Answer 9

increase of one dollar gives decrease of 4 members yes? so if you start at 41 and increase by x dollars you get 41+x dollars per member. decrease for every dollar is 4 members. so if you have 1500 members and increase by x dollars you get 1500-4x members. this equation looks good to me

Answer 10

Thank you for trying :-)

Answer 11

maybe i multiplied wrong hold on.

Answer 12

not it is right. maybe the answer really is $167

Answer 13

can you check?

Answer 14

Nope, not it.

Answer 15

satellite's answer looks right to me.

Answer 16

Sorry, I tried it and it wasn't correct.

Answer 17

i keep trying and it keeps looking right. are you sure you have the problem written correctly?

Answer 18

A health club currently charges its 1500 members monthly membership dues of $41. The board decides to increase the amount of dues charged. The marketing dept. shows that each increase of $1 will result in the loss of 4 clients. How much should the club charge to optimize the revenue from monthly dues?

Answer 19

hold on!
satellite, did you get x = 167?

Answer 20

after you differentiated?

Answer 21

k i am holding

Answer 22

this is not a calc problem. vertex is
\[-\frac{b}{2a}\]

Answer 23

Yep, double checked the problem and you wrote it correctly satellite73.

Answer 24

\[\frac{1336}{8}=167\]

Answer 25

it is the same.

Answer 26

then i say $167 and i am sticking with that

Answer 27

Ugh.

Answer 28

no, 167 is the amount they charge on top of 41 to get maximum profit.
so they charge 167+41

Answer 29

oh for the love of peter. ho ho ho

Answer 30

all together now! facepalm!

Answer 31

sorry.

Answer 32

Hooray! That's it!

Answer 33

yay

Answer 34

Thank you both!!

Answer 35

you are welcome :)

Answer 36

also, satellite, if you differentiate a down facing parabola and equate it to 0, you will get the maxima which happens to be the vertex of the parabola. so yes, this is indeed a calculus problem. in fact, that is why the vertex of the parabola is -b/2a
try it out with this problem and you will see what i'm saying.

Answer 37

y=ax^2+bx+c
dy/dx=2ax+b
0=2ax+b
-b=2ax
x=-b/2a

solution to what the person with the hard name issaying

Answer 38

dhatraditya i mean

Answer 39

lol, yes