Question

A salesperson finds that her sales average 45 cases per store when she visits 5 stores a week. Each time she visits an additional store per week, the average sales per store decreases by 1 case. How many stores should she visit each week if she wants to maximize her sales?

Answer 1

4?

Answer 2

9=45/5

C= cases
s=number of stores
n=additional number of stores

the condition given can be written as
\[9-n={C \over s+n}\]that's just me thinking out loud... don't have the answer yet.

Answer 3

take the derivadtive

Answer 4

of your function and find the maximum and minimum and you will get the answer

Answer 5

good job turing test thumbs up for you

Answer 6

We're on polynomial functions in my class...
Wouldn't we look for h and k using these formulas: h=-B/2A and k=C-B^2/4A?

Answer 7

Idk...

Answer 8

let's derive a formula

Answer 9

great, then I can't use calculus...
either way gotta get C in terms of n though I think

Answer 10

sorry another typo
\[9-n={45\over5+n}\]

Answer 11

is not 45 should be 5

Answer 12

you have the the average

Answer 13

no you are right

Answer 14

C/s=9=45/5
since C/s goes down by the number of additional stores\[{45\over5}-n={45\over5+n}\to 9-n={45\over9+n}\]so I'm pretty sure the formula is right, now let's get it quadratic looking...

Answer 15

now just how did you 9+n

Answer 16

there should be n+1

Answer 17

or n-1 i meant if n represents additional number of store

Answer 18

where did you guys even get this formula?

Answer 19

sorry I keep typing 5 when I mean 9\[9-n={45\over5+n}\]is the formula

Answer 20

not the #s, just the formula where u plugged in the numbers

Answer 21

listen n represents number of additional store which we have in the question but there is a decrease of 1

Answer 22

9 is the average sales for each of the stores (C/s=45/5) in our initial condition,
so in general

rate of sales=cases sold/number of stores
R=C/s

ever time the # of stores goes up by one the rate goes down, so

r-n=C/(s+n)

that is where my formula came from.

Answer 23

now lets get it quadratic-looking:
(9-n)(5+n)=45+4n-n^2=45
4n-n^2=0
which as a maximum at n=2, so the total number of stores to visit is 5+2=7

Answer 24

Ok...
We didn't talk about this in class but it makes sense.

Answer 25

I think you can get the max from one of the formulas you used
h=-b/2a=-4/2(-1)=2

Answer 26

wait shouldnt it be -14n instead of 4n?

Answer 27

-9n + -5n = -14n

Answer 28

(9-n)(5+n)=45+9n-5n-n^2=45+4n-n^2

Answer 29

o nvm u changed one of the signs to a positive

Answer 30

thats not the answer

Answer 31

neither 2 , 4, or 7

Answer 32

hmm...

Answer 33

Can you solve this prob using:
f(x)=ax^2+bx+c
f(x)=a(x-h)+k
h=-b/2a
k=c-(b^2/4a)

Answer 34

well not if I set it up wrong, lol

Answer 35

the 2nd one should be a(x-h)^2+k (my bad)

Answer 36

Cause that's what we've been doing so far in class... Idk why the hw would be different.

Answer 37

You could use that formula on my equation and get n=2 so
total # of stores=7
but you say that is wrong, so it must be set up wrong.

Answer 38

1 and 5 arent the answers either... just tried those out

Answer 39

not sure how:
say she visits 6 stores. One more store means the average goes down to 8, so total sales is 56
say she visits 7 stores. Now the number of stores is 7 and the rate is 7, so total is 49.
if she visits 8 stores then the rate is 6 so the total sales is 56.
hmmm, it looks like 6 stores and 8 stores are both the maximum?

Answer 40

that can't be... what happened?

Answer 41

6 * 8 = 48

Answer 42

oh dear, right so we get 7 again, which is what I originally said...

Answer 43

How is it not seven? hmm...
I must not be seeing something drastic :(

Answer 44

Oh no! I see I misread
45 is the AVERAGE, not 9

Answer 45

\[45-n={225 \over5+n}\]that should do it...

Answer 46

So far these are not the answers:
1-5 and 7

Answer 47

no solve this one
225+40n-n^2=225
n=20 for maximum
total stores=25
Please tell me that's right

Answer 48

yes it is

Answer 49

thank god, do you see how I got it and what mistake I made?

Answer 50

where did you get 225?

Answer 51

total sales/stores=rate of sales per store
C/s=R
C/5=45
C=225
now the formula I had all along will work:\[R-n={C \over s+n}\]\[45-n={225\over5+n}\]All I did was misread that 45 was the total, not the average.

Answer 52

Ok makes sense...
If only my teacher taught us what we need to know for the homework. -_-

Answer 53

wait howd u get 25... im working it out on paper and i get to -n^2+40n=0

Answer 54

\[(45-n)(5+n)=225+45n-5n+n^2=225+40n-n^2\]

Answer 55

yeah i got 225+40n-n^2=225 and i subtracted 225 so i just got 40n-n^2

Answer 56

\[225+40n-n^2=225\]is what we have after multiplying both sides by 5+n which reduces to \[40n-n^2=0\]now use your formula for h=-b/2a

Answer 57

o

Answer 58

we find n=20
so total stores=5+n=25

Answer 59

ok i see. thanks.