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# It is well known that the relationship between the revenue from sales

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Manager
Joined: 17 May 2017
Posts: 130
Schools: ESSEC '20
GPA: 3
It is well known that the relationship between the revenue from sales  [#permalink]

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04 Jul 2017, 03:23
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65% (hard)

Question Stats:

50% (01:50) correct 50% (02:11) wrong based on 51 sessions

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It is well known that the relationship between the revenue from sales of products and the total cost of labor and materials is represented by the function, R(c)= -10c^2+kc+m, where R(c) is the revenue and c is the total cost. When the revenue from sales of products is at its greatest, what is the value of the total cost?

1) k=200
2) m=2,000

approach please unable to understand OE given by them
Math Expert
Joined: 02 Aug 2009
Posts: 7684
Re: It is well known that the relationship between the revenue from sales  [#permalink]

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04 Jul 2017, 07:34
haardiksharma wrote:
It is well known that the relationship between the revenue from sales of products and the total cost of labor and materials is represented by the function, R(c)= -10c^2+kc+m, where R(c) is the revenue and c is the total cost. When the revenue from sales of products is at its greatest, what is the value of the total cost?

1) k=200
2) m=2,000

approach please unable to understand OE given by them

Hi...

the equation here is a quadratic equation and represents a PARABOLA when put to graph.
A) This parabola can be opening upwards and thus will have a minimum value ..
B) or the parabola can be opening downwards and will have a Max value.

Here the NEGATIVE coefficient of c^2 says that it will have a max value..
You should just know that derivative of the equation is equalled to 0 to find that value..
So derivative would be 2*(-10c)+k=0....-20c+k=0..
We are asked for value of C, so we require'k' for that as seen in above equation.
Statement I gives us k, so SUFFICIENT..
Statement II does not talk of k, so insufficient

A
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Re: It is well known that the relationship between the revenue from sales  [#permalink]

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04 Jul 2017, 11:22
1
This requires some in-depth knowledge of quadratic functions, but since $$-10c^2$$ is negative we know that this must be an upside-down parabola (think negative = frown shape); therefore, there's one x-coordinate where the revenue is at its greatest. I think the stretch here is knowing the vertex formula — the vertex (x, y) can be found at $$x = \frac{–b}{2a}$$.

They've masked the question effectively, but you can read it as: When $$y$$ is at its greatest, what is the value of $$x$$? (Revenue is $$y$$; Cost is $$x$$.)

Since you already have the value of $$a$$, all we need is $$b$$ in the quadratic equation to find the x-coordinate of the vertex,

$$x = \frac{–b}{2(-10)}$$
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Joined: 06 Feb 2016
Posts: 3
Re: It is well known that the relationship between the revenue from sales  [#permalink]

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04 Jul 2017, 21:24
Engineers, plz use maxima minima to solve in 10 seconds. If u differentiate the function, R'(c)= 20c+k. Only depends on k. Hence ,,A
Re: It is well known that the relationship between the revenue from sales   [#permalink] 04 Jul 2017, 21:24
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