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Math Help - Help with Area under a curve surplus

  1. #1
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    Help with Area under a curve surplus

    The demand function
    where p = price in dollars and x = sales level in hundreds, is pictured below.


    The area of the grey rectangle in the picture has area = sales level times price = revenue generated by sales.
    The area of the shaded portion under the curve above the rectangle represents the consumers' surplus.

    First find the price, then revenue from sales, then the consumers' surplus for a sales level of 900.

    Note: The consumers' surplus formula involves p(x) and hence x values must be in hundreds. The output of the consumers' surplus integral is in hundreds of dollars though, so be careful with your units!

    Find Price, Revenue from sales and consumer surplus!

    Help this for me please. I have no idea how to start can anyone give me an idea
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  2. #2
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    Quote Originally Posted by v3ndetta View Post
    The demand function
    where p = price in dollars and x = sales level in hundreds, is pictured below.


    The area of the grey rectangle in the picture has area = sales level times price = revenue generated by sales.
    The area of the shaded portion under the curve above the rectangle represents the consumers' surplus.

    for a sales level of 900 ...

    First find the price ... evaluate p(900)

    then revenue from sales ... 900[p(900)]

    consumers' surplus ... \textcolor{red}{\int_0^{900} p(x) \, dx} - 900[p(900)]

    Note: The consumers' surplus formula involves p(x) and hence x values must be in hundreds. The output of the consumers' surplus integral is in hundreds of dollars though, so be careful with your units!
    .
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