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Thread: Polynomial Word Problem, been driving me crazy.

  1. #1
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    Polynomial Word Problem, been driving me crazy.

    Hello, first time poster! I'm currently stuck on this polynomial word problem and really need some help. Before I start showing what I tried heres a link to a picture of the problem. https://imgur.com/a/7WvOd

    Part a) of the problem is asking for a profit of $0 or too just break even. Seems simple (i think). I first set the equation to 0.
    0 = -5x^2 + 550x - 5000
    I solved the problem and got..
    0 = -5(x-10)(x-100)
    So the zeros are x = 10 and x =100, does that mean the company has to spend between 10,000 - 100,000 dollars to break even?

    Part b) If I got 'a' right, to find "How much should be spent on advertising to achieve a maximum profit?" I should do 10 + 100 / 2 which gives me 55 (mid point). Since the question is in thousands of dollars to would cost 50,000 dollars in advertising to achieve a maximum profit?

    Part c) Do I replace x in the equation to 55? Like, P(55) = -5(55)^2 + 550(55) - 5000 = 10,125. So the maximum profit is 10,125 dollars or do I have to multiply 10,125 by 1000 also to get 10,125,000?

    part d) need help with this..

    I'm not sure if I did any of this correctly, if someone could please help me out that would be amazing!
    Last edited by topsquark; Nov 2nd 2017 at 07:23 PM. Reason: LaTeX fix
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  2. #2
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    Re: Polynomial Word Problem, been driving me crazy.

    Quote Originally Posted by Tyler010 View Post
    Hello, first time poster! I'm currently stuck on this polynomial word problem and really need some help. Before I start showing what I tried heres a link to a picture of the problem. https://imgur.com/a/7WvOd

    Part a) of the problem is asking for a profit of $0 or too just break even. Seems simple (i think). I first set the equation to 0.
    0 = -5x^2 + 550x - 5000
    I solved the problem and got..
    0 = -5(x-10)(x-100)
    So the zeros are x = 10 and x =100, does that mean the company has to spend between 10,000 - 100,000 dollars to break even?
    No, it means that the company has to spend **exactly** 10000 dollars or 100000 dollars to "break even". If the company spends "between 10000 and 100000" they will make a profit.

    Part b) If I got 'a' right, to find "How much should be spent on advertising to achieve a maximum profit?" I should do 10 + 100 / 2 which gives me 55 (mid point). Since the question is in thousands of dollars to would cost 50,000 dollars in advertising to achieve a maximum profit?
    If you got 55 why would you say "50,000 dollars" rather than 55,000 dollars?
    (By the way, "10+ 100/2" is equal to 10+ 50= 60. What you are calculating is (10+ 100)/2.)

    Part c) Do I replace x in the equation to 55? Like, P(55) = -5(55)^2 + 550(55) - 5000 = 10,125. So the maximum profit is 10,125 dollars or do I have to multiply 10,125 by 1000 also to get 10,125,000?
    The equation you are given is "$P(t)= -5x^2+ 550x- 50004$" and you are told that P(x) as well as x is "in thousands of dollars. Yes, you have to multiply P(x) by 1000 to get the profit in dollars.

    part d) need help with this..
    This has $x^2$ with a negative coefficient so its graph is a parabola opening downward. You have already calculated that the vertex of the parabola is at (55, 10,125) (where the units are "thousands of dollars"). You also know that the parabola crosses the x-axis at x= 10 and x= 100. That should be enough for you to draw a rough graph. If you want to be more precise, calculate P(x) for many different values of x and use those points to draw the graph. As far as the domain is concerned, the company cannot spend **negative** money.

    I'm not sure if I did any of this correctly, if someone could please help me out that would be amazing!
    Thanks from topsquark
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