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Math Help - Maximizing revenue

  1. #1
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    Maximizing revenue

    A smoothie stand usually sells 150 smoothies per day at $4 each. a business student's research tells her that for every $0.10 decrease in the price, the stand will sell 5 more smoothies per day. Using calculus determine the price at which the smoothies should be sold to maximize revenue. Be very clear when defining your variable(s).
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    Quote Originally Posted by spencersin View Post
    A smoothie stand usually sells 150 smoothies per day at $4 each. a business student's research tells her that for every $0.10 decrease in the price, the stand will sell 5 more smoothies per day. Using calculus determine the price at which the smoothies should be sold to maximize revenue. Be very clear when defining your variable(s).
    Let x represents the number of times the price decrease.

    Price of each smoothie = $ (4 - 0.10x)

    Number of smoothies = (150 + 5x)

    Revenue = (150 + 5x)(4 - 0.10x)

    Now maximize Revenue using calculus.
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    Quote Originally Posted by spencersin View Post
    A smoothie stand usually sells 150 smoothies per day at $4 each. a business student's research tells her that for every $0.10 decrease in the price, the stand will sell 5 more smoothies per day. Using calculus determine the price at which the smoothies should be sold to maximize revenue. Be very clear when defining your variable(s).
    Revenue = (# of smoothies sold)*(price at which they are sold)

    Now, the revenue r(x) = (150 + 5x)(4 - 0.1x)

    since for each $0.1 we take off the price of $4, we increase the number sold by 5 times that number.

    your goal is to maximize r(x)
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    I found that R'(x) = 5-x

    So, x=5 <---critical number

    how can I get the price at which the smoothies should be sold to maximize revenue??
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    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by spencersin View Post
    I found that R'(x) = 5-x

    So, x=5 <---critical number

    how can I get the price at which the smoothies should be sold to maximize revenue??
    ok, is this a maximum point for R(x)?

    remember what price you want to sell at, $(4 - 0.1x)
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