math

during the summer months, sarah makes and sells necklaces on the beach. last summer she sold the nacklaces for $10 each. Her sales averaged 20 per day. Considering a price increase, she took a small survey and found that for every dollar increase, she would lose two sales a day. If the material for each necklaces costs $6, what should her selling price be to maximize the profit?

pls i really need your help for this one. have tried all my best but i don't get it. my teacher didn't teach us yet. she said we should do it on our own

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asked by ted
  1. If your teacher has not taught anything yet, then try the following, which works for anyone:

    Make a table of the number of necklaces sold and the profit.

    At $10 a necklace, she sells 20 a day with a profit of $4 each, so her net profit is $4*20=$80/day.

    At $11 a necklace, she sells 18 a day with a profit of $5 each, so her net profit is $5*18=$90/day.

    At $12 a necklace, she sells 16 a day with a profit of $6 each, so her net profit is $6*16=$96/day.

    ...
    Continue this way until the profit drops, then take the highest profit.

    If I were you, I would go for the $0.50 increase/decrease once the highest profit is known.

    Post your answer for a check if you wish.

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  2. at $19 a necklace, she sells 2 a day, so her net profit is $2.
    is that right

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    posted by ted
  3. At $19 a necklace, her profit is $19-$6=$13 for each necklace she sells. So her net profit is $13*2 necklaces = $26.

    But $26 is lower than $96 when she would sell them at $12 a necklace.

    So continue with $13, $14, ... until the net profit goes down. Then choose the price that would give the highest profit.

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