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Math Help - Question about linear functions with several variables

  1. #1
    m58
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    Question about linear functions with several variables

    Hi guys,

    Just wanted to check over if I understood the following problems correctly:

    1) Bill has a fixed cost of $215 per day to run his art business. Unit costs are .65 per paintbrush, which he then resells at 1.75 per brush. Express his daily profit in number of brushes sold.

    So, is this correct?:
    y = profit
    x = each brush sold
    .65 + 1.75 = 2.4
    2.4x + 215 = y

    2) Jake's publishing company sells books at 14.5 per unit. His publishing costs are 1400 per day, and he incurs unit costs of 3.85 each. Due to a new publishing process, his fixed costs increase to 1725 (this reduces the unit cost, making it 2.7 each). Express Jake's increase in profit as a linear function of sold books and publishing costs.

    So I would do:

    y = total units
    x= each additional unit

    14.5 + 3.85 = 18.35
    1400 + 18.35x = y


    14.5 + 2.7 = 17.2
    1725 + 17.2x = y

    (1725 + 17.2x) - (1400 + 18.35x) = 325 - 1.15x

    Thanks!
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  2. #2
    Master Of Puppets
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    Re: Question about linear functions with several variables

    Quote Originally Posted by m58 View Post
    Hi guys,

    Just wanted to check over if I understood the following problems correctly:

    1) Bill has a fixed cost of $215 per day to run his art business. Unit costs are .65 per paintbrush, which he then resells at 1.75 per brush. Express his daily profit in number of brushes sold.

    Let x be the number of paintbrushes

    Profit = Revenue - Cost

    Profit = 1.75x - (215+0.65x) = ....

    can you finish it?
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  3. #3
    m58
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    Re: Question about linear functions with several variables

    Hmm... so it would be:

    y = 1.75x - (215 + .65x) -> 1.1x - 215
    So if he sold 5 brushes, his profit would be -209.5?

    I should have put that the problem wants "the daily profit as a linear function of brushes sold". My bad.
    Last edited by m58; September 12th 2011 at 03:53 PM.
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  4. #4
    m58
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    Re: Question about linear functions with several variables

    Also, just figured out the second problem using your method, pickslides:

    14.5x - (1400 + 3.85x) -> 10.65x - 1400
    14.5x - (1725 - 8.7x) -> 11.8x - 1725

    (11.8x - 1725) - (10.65x - 1400) = 1.15x - 325
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  5. #5
    Master Of Puppets
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    Re: Question about linear functions with several variables

    Quote Originally Posted by m58 View Post
    y = 1.75x - (215 + .65x) -> 1.1x - 215
    So if he sold 5 brushes, his profit would be -209.5?
    Yep, nice work!
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