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Math Help - Word problem: Cost function, Revenue Function, Profit function.

  1. #1
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    Word problem: Cost function, Revenue Function, Profit function.

    Hey guys I have a word problem and I was wondering if you could check my work. A factory can product 1,000 bottles per hour. The machine (with setup) cost $3,000,000, whilst each bottle costs .5 cents (labor,materials, etc.) to make. The machine runs 10 hours per day. If each bottle sells for .65 cents, express the cost, revenue and profit for running the factory for X days. After how many days will the factory break even?

    Cost function, C(x) = 3,000,000 + .05(10000X)
    = 3,000,000 + 5000X
    Revenue function, R(x) = .65(10000X)
    = 6500X
    Profit function, P(x) = 6500X - 3000000 + 5000X
    = 11500X - 3000000
    Break Even: 3000000 = 11500X
    So in approximately 261 days the factory will break even.

    Am I right?
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    Re: Word problem: Cost function, Revenue Function, Profit function.

    Quote Originally Posted by hollylovespunk View Post
    Hey guys I have a word problem and I was wondering if you could check my work. A factory can product 1,000 bottles per hour. The machine (with setup) cost $3,000,000, whilst each bottle costs .5 cents (labor,materials, etc.) to make. The machine runs 10 hours per day. If each bottle sells for .65 cents, express the cost, revenue and profit for running the factory for X days. After how many days will the factory break even?

    Cost function, C(x) = 3,000,000 + .05(10000X)
    = 3,000,000 + 5000X
    Revenue function, R(x) = .65(10000X)
    = 6500X
    Profit function, P(x) = 6500X - 3000000 + 5000X
    = 11500X - 3000000
    Break Even: 3000000 = 11500X
    So in approximately 261 days the factory will break even.

    Am I right?
    no ...

    P(x) = R(x) - C(x) = 6500x - (3,000,000 + 5000x)

    try again
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    Re: Word problem: Cost function, Revenue Function, Profit function.

    So its 1500X. So the factory would break even after 2000 days?
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    Re: Word problem: Cost function, Revenue Function, Profit function.

    after looking again, I notice you've also made one significant arithmetic error in your original function.

    .05(10000x) \ne 5000x
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    Re: Word problem: Cost function, Revenue Function, Profit function.

    Why does 0.5 multiplied by 10000X not equal 5000X?
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    Re: Word problem: Cost function, Revenue Function, Profit function.

    Quote Originally Posted by hollylovespunk View Post
    Why does 0.5 multiplied by 10000X not equal 5000X?
    0.5 cents = 0.005 dollars
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    Re: Word problem: Cost function, Revenue Function, Profit function.

    Thanks for pointing that out. How does the set up look?
    Last edited by hollylovespunk; September 18th 2011 at 02:36 PM.
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    Re: Word problem: Cost function, Revenue Function, Profit function.

    Quote Originally Posted by hollylovespunk View Post
    Thanks. How does the rest look?f
    make the correction, solve the problem and then I'll respond.
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    Re: Word problem: Cost function, Revenue Function, Profit function.

    C(x) = 3000000 + 500X

    R(x) = 6500X

    P(x) = 6500X - (3000000 + 500X)
    = 6000X - 3000000
    Break Even: 6000X = 3000000

    The factory would break even after 500 days
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  10. #10
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    Re: Word problem: Cost function, Revenue Function, Profit function.

    The machine (with setup) cost $3,000,000, whilst each bottle costs .5 cents (labor,materials, etc.) to make. The machine runs 10 hours per day. If each bottle sells for .65 cents, express the cost, revenue and profit for running the factory for X days.
    0.5 cents = 0.005 dollars ... 0.65 cents = 0.0065 dollars

    that means a profit of only 0.0015 dollars per bottle x 10000 = $15.00 per day

    going to take an unreasonably long time to break even with 3 million dollars

    something's not right with the problem statement ... recheck the bottle cost and selling prices.
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    Re: Word problem: Cost function, Revenue Function, Profit function.

    I am sorry. I just realized what I did. The problem says 5 cents. I entered it incorrectly as 0.5 cents
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    Re: Word problem: Cost function, Revenue Function, Profit function.

    Quote Originally Posted by hollylovespunk View Post
    I am sorry. I just realized what I did. The problem says 5 cents. I entered it incorrectly as 0.5 cents
    how about the selling price ... 0.65 cents, 6.5 cents, or 65 cents?
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    Re: Word problem: Cost function, Revenue Function, Profit function.

    The problem says 65 cents I should really work smart and not hard
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    Re: Word problem: Cost function, Revenue Function, Profit function.

    Well here is my solution:

    C(x) = 3000000 + (10000x) .05
    = 3000000 + 500x

    R(x) = .65(10000x)
    = 6500x

    P(x) = R(x) - C(x)
    = 6500x - 3000000 - 500x
    = 6000x - 3000000

    Break even: R(x) = C(x)
    6500x = 3000000 + 500x
    6000x = 3000000
    Break even after 500 days.

    Looks good?
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  15. #15
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    Re: Word problem: Cost function, Revenue Function, Profit function.

    Quote Originally Posted by hollylovespunk View Post
    Well here is my solution:

    C(x) = 3000000 + (10000x) .05
    = 3000000 + 500x

    R(x) = .65(10000x)
    = 6500x

    P(x) = R(x) - C(x)
    = 6500x - 3000000 - 500x
    = 6000x - 3000000

    Break even: R(x) = C(x)
    6500x = 3000000 + 500x
    6000x = 3000000
    Break even after 500 days.

    Looks good?
    that's fine.
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