Question

You have invested $30,000 and started a business writing greeting cards. Supplies cost $0.02 per card and you are selling each card for $0.50. (Let c represent the number of cards produced and sold.)
a. Write the cost function, c
b. Write the revenue function, R
c. Determine the break-even point. (the entire ordered pair)

Answer 1

If supplies cost $0.02 per card and you make 5 cards, how much does that cost you?

Answer 2

$5.00

Answer 3

I need help on this one

Answer 4

Sorry for the break. How did you get $5 cost to make 5 cards?

Answer 5

.02x5x0.50

Answer 6

or would it be 2.50

Answer 7

Ok, sorry. I was talking about just how much it costs, ignoring how much you make off of it. So if we ignore how much you sell the card for, how do you find how much it cost you to make 5 cards?

Answer 8

.02x5=10

Answer 9

Right. So for a given number of cards c, how much does it cost just to make that number of cards?

Answer 10

.10x5=.50

Answer 11

so the cost function would be 600 cards produced and sold

Answer 12

Er... Wait. No. If you calculated the cost of making 5 cards as 0.02x5, then the cost of making c cards is 0.02c, right?

Answer 13

Now, the cost function also takes into account starting costs and then profit made. So, if you sell 5 cards (ignore how much it costs to actually make them), how much do you get for them?

Answer 14

yes but c has to represent the number of cards produced and sold

Answer 15

Right, we're dealing with the sold part right now. Call it `n' instead if that makes more sense to you.

Answer 16

$1.00

Answer 17

to make 5 cards

Answer 18

So if it costs 0.02n to make n cards, and you get 0.5m when you sell m cards, if you make and cell c cards, how much do you get in total?

Answer 19

$50

Answer 20

Well we're talking about some number c of cards, so it can't be an absolute number; it has to be in terms of c.

Answer 21

5x.50=2.50

Answer 22

Yes, but for some arbitrary number of cards, c, how much would we make total, including how much it cost us to make the cards and how much we made selling them?

Answer 23

it is costing .02 per card to make and selling them for .50 each. $1.00 to make 5 cards and if we sell 5 cards at .50 then the total would be 3.50

Answer 24

Still not clear how you're getting that it costs $1 to make 5 cards. 5 x 0.02 is not $1, it's $0.10.

Answer 25

oh putting my decimal in the wrong place.
then it would be $5.00 to make 5 cards

Answer 26

So it costs you $0.10 to make the five cards, you get $3.50 for selling them, so the net amount that you make is $3.50 - $0.10 = $3.40.

You can express this by writing an equation for your net income, N:

N = 0.5c - 0.02c

Then, you have to subtract your initial costs so that you can find the point at which you break even:

N = 0.5c - 0.02c - 30000

Then the point where you break even is where N = 0, so you can solve for c, the number of cards where you have made the same amount as you have spent.

Answer 27

I am selling each card for .50

Answer 28

c(x)=30,000+.02x
r(x)=.50x
.50x=30,000+.02x
-.02= -.02x
.48x=30,000
.48/.48=30,000/.48= 625 cards

Answer 29

is this right???

Answer 30

then the break even point is
.50(625)=(625, 312.50)

Answer 31

is this right???

Answer 32

Close -- you messed up your division. 30000/0.48 is 62500. The rest is perfect!

Answer 33

so my break even point in (62500, 31250)

Answer 34

Sounds about right.

Answer 35

or should it be (625.00,312.50)