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anonymous

  • 5 years ago

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)

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  1. shadowfiend
    • 5 years ago
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    If supplies cost $0.02 per card and you make 5 cards, how much does that cost you?

  2. anonymous
    • 5 years ago
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    $5.00

  3. anonymous
    • 5 years ago
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    I need help on this one

  4. shadowfiend
    • 5 years ago
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    Sorry for the break. How did you get $5 cost to make 5 cards?

  5. anonymous
    • 5 years ago
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    .02x5x0.50

  6. anonymous
    • 5 years ago
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    or would it be 2.50

  7. shadowfiend
    • 5 years ago
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    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?

  8. anonymous
    • 5 years ago
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    .02x5=10

  9. shadowfiend
    • 5 years ago
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    Right. So for a given number of cards c, how much does it cost just to make that number of cards?

  10. anonymous
    • 5 years ago
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    .10x5=.50

  11. anonymous
    • 5 years ago
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    so the cost function would be 600 cards produced and sold

  12. shadowfiend
    • 5 years ago
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    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?

  13. shadowfiend
    • 5 years ago
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    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?

  14. anonymous
    • 5 years ago
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    yes but c has to represent the number of cards produced and sold

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

  16. anonymous
    • 5 years ago
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    $1.00

  17. anonymous
    • 5 years ago
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    to make 5 cards

  18. shadowfiend
    • 5 years ago
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    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?

  19. anonymous
    • 5 years ago
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    $50

  20. shadowfiend
    • 5 years ago
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    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.

  21. anonymous
    • 5 years ago
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    5x.50=2.50

  22. shadowfiend
    • 5 years ago
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    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?

  23. anonymous
    • 5 years ago
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    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

  24. shadowfiend
    • 5 years ago
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    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.

  25. anonymous
    • 5 years ago
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    oh putting my decimal in the wrong place. then it would be $5.00 to make 5 cards

  26. shadowfiend
    • 5 years ago
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    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.

  27. anonymous
    • 5 years ago
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    I am selling each card for .50

  28. anonymous
    • 5 years ago
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    c(x)=30,000+.02x r(x)=.50x .50x=30,000+.02x -.02= -.02x .48x=30,000 .48/.48=30,000/.48= 625 cards

  29. anonymous
    • 5 years ago
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    is this right???

  30. anonymous
    • 5 years ago
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    then the break even point is .50(625)=(625, 312.50)

  31. anonymous
    • 5 years ago
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    is this right???

  32. shadowfiend
    • 5 years ago
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    Close -- you messed up your division. 30000/0.48 is 62500. The rest is perfect!

  33. anonymous
    • 5 years ago
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    so my break even point in (62500, 31250)

  34. shadowfiend
    • 5 years ago
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    Sounds about right.

  35. anonymous
    • 5 years ago
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    or should it be (625.00,312.50)

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