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  1. #1
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    equation problem

    hello i would appreciate if someone could kindly look into the problem and help me get the solution:

    Q) the profit, P, of a video company (in thousands of dollars) is given by P(x)=-5x2 + 550x - 5000, where x is the amount spent on advertising, in thousands of dollars.

    a) Determine the amount spent on advertising that will result in a profit of $0. In other words,you will determine the amount that must be spent on advertising in order for the company to "break even." Describe the relationship between these values and the graph of P(x)
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  2. #2
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    Re: equation problem

    Quote Originally Posted by allison View Post
    a) Determine the amount spent on advertising that will result in a profit of $0. In other words,you will determine the amount that must be spent on advertising in order for the company to "break even." Describe the relationship between these values and the graph of P(x)
    The company will break even when the profit P(x) = 0. So we have an equation:

    P(x) = 0

    \Rightarrow-5x^2+550x-5000 = 0

    Now solve for x.
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  3. #3
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    Re: equation problem

    Quote Originally Posted by allison View Post
    hello i would appreciate if someone could kindly look into the problem and help me get the solution:

    Q) the profit, P, of a video company (in thousands of dollars) is given by P(x)=-5x2 + 550x - 5000, where x is the amount spent on advertising, in thousands of dollars.

    a) Determine the amount spent on advertising that will result in a profit of $0. In other words,you will determine the amount that must be spent on advertising in order for the company to "break even." Describe the relationship between these values and the graph of P(x)
    set P(x) = 0 and solve the quadratic for x

    also, please post algebra questions in the algebra forum, not in the introduction lobby.
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    Re: equation problem

    thank you so much guys! that was really quick

    So, for x.. what i have done is

    - 5x2 + 550x - 50000
    or -5 (x2-110x+1000)
    or, -5 (x-100)(x-10)
    or,x=100, or x=10

    i guess i have to findout the mid-value as well inorder to get the amt.
    so, mid-value is x = 100+10 divided by 2
    so x = 55

    am i right, guys?? pls help
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    Re: equation problem

    thnx skeeter! i am a new user so didn't pay much attention to it ,i will make sure next time i will posts my queries into proper forum. could you kindly look into my answer whether that is how it should be
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    MHF Contributor Reckoner's Avatar
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    Re: equation problem

    Quote Originally Posted by allison View Post
    or,x=100, or x=10
    This is correct.

    Quote Originally Posted by allison View Post
    i guess i have to findout the mid-value as well inorder to get the amt.
    so, mid-value is x = 100+10 divided by 2
    No. We are looking for what value(s) of x make P(x) zero. You have found that there are two values for which this occurs: x=10 and x=100. Both of these are break-even points. The first solution is the minimum amount of money that must be spent on advertising in order to turn a profit, and the second solution is the maximum amount of money that can be spent on advertising before the advertising costs outweigh the increased revenue.

    Finding the midpoint of these two values actually gives you the x-coordinate of the vertex of this parabola, which in this problem represents the amount of money that must be spent to get the maximum profit.
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    Re: equation problem

    Quote Originally Posted by Reckoner View Post
    This is correct.


    No. We are looking for what value(s) of x make P(x) zero. You have found that there are two values for which this occurs: x=10 and x=100. Both of these are break-even points. The first solution is the minimum amount of money that must be spent on advertising in order to turn a profit, and the second solution is the maximum amount of money that can be spent on advertising before the advertising costs outweigh the increased revenue.

    Finding the midpoint of these two values actually gives you the x-coordinate of the vertex of this parabola, which in this problem represents the amount of money that must be spent to get the maximum profit.

    Thank you so much for your time ! that was really helpful.
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    Re: equation problem

    Hi, just a quick question
    how can i insert a division line : i want to insert a line so that i can put 1/2 or 1 over 2. i would like the 1 to be right on top of the 2 with a line separating the numbers in the middle.

    thanks for the help!
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  9. #9
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    Re: equation problem

    Hi, just a quick question
    how can i insert a division line : i want to insert a line so that i can put 1/2 or 1 over 2. i would like the 1 to be right on top of the 2 with a line separating the numbers in the middle.

    thanks for the help!
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  10. #10
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    Re: equation problem

    Quote Originally Posted by Reckoner View Post
    This is correct.


    No. We are looking for what value(s) of x make P(x) zero. You have found that there are two values for which this occurs: x=10 and x=100. Both of these are break-even points. The first solution is the minimum amount of money that must be spent on advertising in order to turn a profit, and the second solution is the maximum amount of money that can be spent on advertising before the advertising costs outweigh the increased revenue.

    Finding the midpoint of these two values actually gives you the x-coordinate of the vertex of this parabola, which in this problem represents the amount of money that must be spent to get the maximum profit.
    Hi, i got the maximum profit as :
    mid-value is x = 100+10 divided by 2
    so x = 55
    P(x)= -5x2 + 550x - 5000
    P(55)= - 5(55)2 + 550(55) - 5000
    = 15125 + 30250 - 5000
    = 45375 - 5000
    =40,375
    The maximum profit is $40,375.

    Can you help me graph the function and state the domain, please.
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  11. #11
    MHF Contributor Reckoner's Avatar
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    Re: equation problem

    Quote Originally Posted by allison View Post
    P(55)= - 5(55)2 + 550(55) - 5000
    P(55)=-5\cdot55^2+550\cdot55-5000

    =-15\,125+30\,250-5000

    =10\,125

    Quote Originally Posted by allison View Post
    Can you help me graph the function and state the domain, please.
    The simplest way to sketch a graph is to plot a few points. We already have the coordinates of several important features of this parabola: the vertex is at (55, 10\,125), the x-intercepts are at (10, 0) and (100, 0). Setting x=0 shows us that our y-intercept is at (0, -5000). Now plot the points, and connect them with a smooth parabola.

    For the domain, note that this is a polynomial function. What is the domain of a polynomial function?
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