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Math Help - How many items to produce to earn a profit?

  1. #1
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    How many items to produce to earn a profit?

    A certain manufacturer produces items for which the production costs consists of annual fixed costs totaling $130,000 and variable costs averaging $8 per item. If the manufacturer's selling price per item is $15, how many items must the manufacturer produce and sell to earn an annual profit of $150,000?

    Is my answer correct? My answer is 40,000. The way I got this was

    130,000 +8 (x) + 150,000 = 15 (x)
    280,000 + 8x = 15x
    280,000 = 7 x
    x= 40,000
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by thecapaccino View Post
    A certain manufacturer produces items for which the production costs consists of annual fixed costs totaling $130,000 and variable costs averaging $8 per item. If the manufacturer's selling price per item is $15, how many items must the manufacturer produce and sell to earn an annual profit of $150,000?

    Is my answer correct? My answer is 40,000. The way I got this was

    130,000 +8 (x) + 150,000 = 15 (x)
    280,000 + 8x = 15x
    280,000 = 7 x
    x= 40,000

    i like your way, here's another (more explanatory) approach

    let revenue be R(x)
    let cost be C(x)
    let profit be P(x)

    the revenue is the money earned from selling x units, so R(x) = 15x

    the cost is...well, the cost. we pay 130000 fixed cost no matter what, plus $8 per item, so C(x) = 8x + 130000

    The profit is the money we make, that is the revenue minus the cost, so
    P(x) = R(x) - C(x)
    => P(x) = 15x - 8x - 130000
    => P(x) = 7x - 130000

    we want a profit of 150000, that is, we want P(x) = 150000

    => P(x) = 150000 = 7x - 130000
    => 280000 = 7x
    => x = 40000

    so you are correct
    Last edited by Jhevon; April 17th 2007 at 09:06 PM.
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  3. #3
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    Yeah

    The cobwebs are coming off the brain.

    Thanks!!! Actually, I like your way...more analytical....

    Cheers
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  4. #4
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by thecapaccino View Post
    The cobwebs are coming off the brain.

    Thanks!!! Actually, I like your way...more analytical....

    Cheers
    shorter methods are usually more elegant to me. but i usually use long methods when i'm on this site, since those methods explain the logic better
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