math

Liam is the founder and president of the Justin Bieber Fan Club. As a fundraiser, the JBFC sells chocolate-flavored spaghetti sauce. The current price is $6.40 per jar and their average monthly sales are 250 jars. They are considering raising prices and have been surveying customers to determine if this is a good decision. They have determined that every $0.10 increase in price will cost them 5 sales per month. Determine the range of prices that they could charge in order to make at least $1500 per month. (I have tried all I can think of but I can't figure out how to solve this. Any help would be very useful. I've put it into the equation 1500=(250-5r) (6.40+0.10r)

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  1. Your equation looks good. So, just solve it and you get

    (250-5r) (6.40+0.10r) >= 1500
    -.5r^2 - .7r + 1600 >= 1500
    .5r^2 + .7r - 100 >= 0
    Now, solve the left side using the quadratic formula, and you find that

    .5r^2 + .7r - 100 = 0 at
    x = -22.8 and 8.8

    Between those two roots, the function is positive, so since we are dealing with the real world, we need r>=0, and we have

    .5r^2 + .7r + 1600 >= 1500
    for 0 <= r <= 8

    Now you can figure the actual price range.

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    posted by Steve
  2. I haven't learned how to find a function. Do you mind walking me through it?

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    posted by Rachelle
  3. Excuse me? You developed your own function. The price after r rate increases is

    6.40 + 0.1r

    so, for r=0, the price is 6.40
    for r=8, the price is 6.40+.1*8 = 7.20

    Between those two prices, she'll make at least $1500.

    Take a look at

    http://www.wolframalpha.com/input/?i=plot+y%3D%28250-5r%29+%286.40%2B0.10r%29%2C+y%3D1500

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    posted by Steve

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