Question

Susie wants to start making and selling bracelets. Her costs are the large sum of money that includes her initial investment and the cost of materials for each bracelet. She has already planned how much she is going to sell her bracelets for. Explain how Susie can set up a system of equations to predict when she will start to make a profit.

Answer 1

@Ahsome

Answer 2

hello

Answer 3

hi

Answer 4

Cost = Initial Investment + Materials

Answer 5

What is the profit defines as?

Answer 6

right

Answer 7

do u have to make two quations

Answer 8

yes

Answer 9

We are looking for the point where "Susie starts to make a profit"

Answer 10

so from the above we want

Profit = 0 = (selling revenue) - (materials cost)

Answer 11

When she starts to make a profit, at that instant, the materials cost and the amount sold will be the same, she will be at profit = 0, breaking even

Answer 12

get that?

Answer 13

So we need to define some variables....

Answer 14

okay

Answer 15

So lets set up the first equation...

Money generated = price per bracelet x number of bracelets sold

Answer 16

pick variables for each one

Answer 17

m=pb*nb

Answer 18

who is susie. is she sexy

Answer 19

just kidding now lets start with this problem

Answer 20

ok, lets call each one by a single variable... how about this..

I(x) = income generated from selling x bracelets
P = selling price of one bracelet
X = # of bracelets sold

Income generated = price per bracelet * bracelets sold

I(x) = P*X

Answer 21

Now, we need an equation for the money going OUT, the costs

Let C(x) = cost incurred from selling x bracelets

Answer 22

okay

Answer 23

The cost to make bracelets = Materials per bracelet + initial investment

Answer 24

C(x) = cost to make x bracelets
V = Initial Investment amount
b = cost per bracelet
x = number of bracelets sold

C(x) = b*x + V

Answer 25

So those are the two equations, C(x) - cost to make x bracelets, and I(x) - Income made from selling x bracelets

Answer 26

THey are asking when she starts to make a profit, in other words, when is she at the Break Even point.

Answer 27

this is starting to make sense :)

Answer 28

really terrible at math

Answer 29

cost = income (breaking even)

C(x) = I(x)

\(\large\color{red}{ {\bf }(b*x) +V = (P*x) }\)

I(x) = income generated from selling x bracelets
P = selling price of one bracelet
x = # of bracelets sold

C(x) = cost to make x bracelets
V = Initial Investment amount
b = cost per bracelet
x = number of bracelets sold

Answer 30

So with the variables we defined,
She will start making money when the income coming in equals the cost going out.

\(\large\color{blue}{ {\bf I(x) = C(x)} }\)

Using both the equations with the variables we defined, you get the red equation above.
With a little rearranging...

\(\Huge\color{red}{ {\bf P*x~=~b*x~+~V} }\)

For the number of bracelets sold, X, Susie will start to make a profit when the value of P*x equals the value of [b*x + V].
In other words, the money made from selling the bracelets at a certain price, will need to be equal to the cost of making that many bracelets plus her initial investment V.

Answer 31

I know it is a lot, let me know if you dont understand something.

Answer 32

yes i do understand!!!! finally someone help me understand.

Answer 33

okay i am trying but my computers acting up. but i will do so!!! You are a big help!!!!! thanks:)

Answer 34

no prob, let me know if ya need anything else whenever.

Answer 35

you bet!!!!