Algebra

david makes and sells chairs. The function p(x)=-10x^2+100x-210, graphed below, indicated how much profit he makes in a month if he sells the chairs for 10-x dollars each. what should david charge per chair to make the maximum profit, and what is the maximum profit he can make in a month?

What do I do?? I'm really confused over this!!! Please help!!!!

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  1. the maximum profit is at the vertex of the parabola. As you know, the vertex of the parabola

    ax^2+bx+c

    is at

    x = -b/2a
    y = (b^2-4ac)/4a

    So, for

    -10x^2+100x-210

    the vertex is at (5,40)

    Since x=5, the price is 10-x = 5 as well.

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  2. p(x) is a parabola opening down(sheds water)
    therefore the vertex is at the top p
    So use complete square to find vertex (if you do not know any calculus)

    -10 x^2 + 100 x = p + 210

    x^2 - 10 x = - (1/10)(p+210)
    x^2 - 10 x + 25= -(1/10)(p+210)+25

    (x-5)^2 = -(1/10)(p+210-250)
    x = 5 and p = 40
    10-5 = 5
    max p = 40

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  3. The answer is A. $40 at $5 per chair.

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