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Thread: Creating a Piecewise Function

  1. #1
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    Question Creating a Piecewise Function

    1.Bob is planning a convention and he is planning for potential attendance levels from 1000 people all the way up to 20000 people. He has the following costs. He is hiring one a speaker who is charging $5000 for the service, regardless of how many people attend the convention. He can secure a convention center large enough for 6000 people (but no more) for $85,000, or a center that can accommodate 20000 people for $300,000. The variable cost per fan is $15.00, which includes beverages and food. Create the piecewise function.

    This is the problem I am having trouble with. It would be amazing if someone could help me!
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  2. #2
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    Re: Creating a Piecewise Function

    Quote Originally Posted by TheRipePine View Post
    1.Bob is planning a convention and he is planning for potential attendance levels from 1000 people all the way up to 20000 people. He has the following costs. He is hiring one a speaker who is charging \$5000 for the service, regardless of how many people attend the convention. He can secure a convention center large enough for 6000 people (but no more) for \$85,000, or a center that can accommodate 20000 people for \$300,000. The variable cost per fan is \$15.00, which includes beverages and food. Create the piecewise function.

    This is the problem I am having trouble with. It would be amazing if someone could help me!
    escaped \$ signs to make more readable
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  3. #3
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    Re: Creating a Piecewise Function

    Quote Originally Posted by TheRipePine View Post
    1.Bob is planning a convention and he is planning for potential attendance levels from 1000 people all the way up to 20000 people. He has the following costs. He is hiring one a speaker who is charging \$5000 for the service, regardless of how many people attend the convention. He can secure a convention center large enough for 6000 people (but no more) for \$85,000, or a center that can accommodate 20000 people for \$300,000. The variable cost per fan is \$15.00, which includes beverages and food. Create the piecewise function.

    This is the problem I am having trouble with. It would be amazing if someone could help me!
    let $n$ be the number of fans that attend

    $TotalCost(n) = 5000 + 15n +\begin{cases}85000 &n\leq 6000 \\300000 &6000 < n \leq 20000 \end{cases}$

    or

    $TotalCost(n) = \begin{cases}90000 + 15n &n \leq 6000 \\ 305000+15n &6000 < n \leq 20000 \end{cases}$

    Of course Bob has to select one or the other prior to the convention, it's not like he can magically swap convention centers once the number of attendees hits 6000.
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  4. #4
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    Re: Creating a Piecewise Function

    Oh my goodness! Thank you so much!!
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