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# It’s well known that a company's profit=20,000x-25x^2, where x is the

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Math Revolution GMAT Instructor
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It’s well known that a company's profit=20,000x-25x^2, where x is the [#permalink]

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Updated on: 12 Oct 2016, 03:58
2
7
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Difficulty:

45% (medium)

Question Stats:

64% (01:26) correct 36% (01:34) wrong based on 232 sessions

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It’s well known that a company's profit=20,000x-25x^2, where x is the number of workers. If the profit of the company is the greatest, what is the value of x?

A. 50
B. 100
C. 150
D. 250
E. 400

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"Only $99 for 3 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" Originally posted by MathRevolution on 12 Oct 2016, 03:31. Last edited by Bunuel on 12 Oct 2016, 03:58, edited 1 time in total. Renamed the topic and edited the question. Manager Status: The first one did not go in accordance with my plans Joined: 15 Aug 2016 Posts: 63 Location: India GMAT 1: 660 Q51 V27 GMAT 2: 690 Q48 V37 GPA: 4 WE: Consulting (Internet and New Media) Re: ) It’s well known that a company's profit=20,000x-25x^2, where [#permalink] ### Show Tags 12 Oct 2016, 03:59 MathRevolution wrote: It’s well known that a company's profit=20,000x-25x^2, where x is the number of workers. If the profit of the company is the greatest, what is the value of x? A. 50 B. 100 C. 150 D. 250 E. 400 E - Used plugin after plotting a graph of this equation. Board of Directors Status: QA & VA Forum Moderator Joined: 11 Jun 2011 Posts: 3622 Location: India GPA: 3.5 WE: Business Development (Commercial Banking) Re: It’s well known that a company's profit=20,000x-25x^2, where x is the [#permalink] ### Show Tags 12 Oct 2016, 11:16 1 MathRevolution wrote: It’s well known that a company's profit=20,000x-25x^2, where x is the number of workers. If the profit of the company is the greatest, what is the value of x? A. 50 B. 100 C. 150 D. 250 E. 400 So, $$Profit = 20000x - 25x^2$$ Or, $$Profit = x ( 20000 - 25x )$$ Quote: Where x is the number of workers. If the profit of the company is the greatest, what is the value of x? Now, to maximize profit we must minimize : ( 20000 - 25x ) Among the given options only (E) is the highest value for x , that can maximize the Final Value (Profit ) So, Answer will be (E) _________________ Thanks and Regards Abhishek.... PLEASE FOLLOW THE RULES FOR POSTING IN QA AND VA FORUM AND USE SEARCH FUNCTION BEFORE POSTING NEW QUESTIONS How to use Search Function in GMAT Club | Rules for Posting in QA forum | Writing Mathematical Formulas |Rules for Posting in VA forum | Request Expert's Reply ( VA Forum Only ) Manager Joined: 28 Jun 2016 Posts: 207 Location: Canada Concentration: Operations, Entrepreneurship It’s well known that a company's profit=20,000x-25x^2, where x is the [#permalink] ### Show Tags 12 Oct 2016, 16:40 2 2 Alternate approach: To find Max or Min of a polynomial f(x), Equate f'(x)=0 f(x) = 20,000x-25x^2 Differentiate f(x) f'(x) = 20,000 - 25*2*x = 0 50x = 20,000 x=400 D Note: To confirm whether x is maximum or minimum, substitute x in f''(x) If f''(x) <0, then f(x) is maximum If f''(x) >0, then f(x) is minimum In this case, f''(x)= -50 < 0 Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 5825 GMAT 1: 760 Q51 V42 GPA: 3.82 It’s well known that a company's profit=20,000x-25x^2, where x is the [#permalink] ### Show Tags 13 Oct 2016, 07:33 It’s well known that a company's profit=20,000x-25x^2, where x is the number of workers. If the profit of the company is the greatest, what is the value of x? A. 50 B. 100 C. 150 D. 250 E. 400 _________________ MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only$99 for 3 month Online Course"
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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 5825
GMAT 1: 760 Q51 V42
GPA: 3.82
Re: It’s well known that a company's profit=20,000x-25x^2, where x is the [#permalink]

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17 Oct 2016, 00:33
==>In general, from y=ax2+bx+c, the value of y from symmetric axis, x=-b/2a is the least or the greatest. For the profit has to be the greatest, x=-20,000/2(-25) = 400, hence the greatest profit. The answer is E.
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Re: It’s well known that a company's profit=20,000x-25x^2, where x is the [#permalink]

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11 Nov 2016, 03:06
Abhishek009 wrote:
MathRevolution wrote:
It’s well known that a company's profit=20,000x-25x^2, where x is the number of workers. If the profit of the company is the greatest, what is the value of x?

A. 50
B. 100
C. 150
D. 250
E. 400

So, $$Profit = 20000x - 25x^2$$

Or, $$Profit = x ( 20000 - 25x )$$

Quote:
Where x is the number of workers. If the profit of the company is the greatest, what is the value of x?

Now, to maximize profit we must minimize : ( 20000 - 25x )

Among the given options only (E) is the highest value for x , that can maximize the Final Value (Profit )

Hi,
Sorry, slightly unclear on the highlivhted portion above, but should we not try to maximise the highlighted portion as bigger the multiple of x, higher the value of the profit. Please can anyone let me know what am i missing here.

Thanks
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Re: It’s well known that a company's profit=20,000x-25x^2, where x is the [#permalink]

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12 Nov 2016, 06:34
1
2
MathRevolution wrote:
It’s well known that a company's profit=20,000x-25x^2, where x is the number of workers. If the profit of the company is the greatest, what is the value of x?

A. 50
B. 100
C. 150
D. 250
E. 400

Notice the given formula P = 20,000x - 25x^2 is a quadratic function. Furthermore, the graph of this function will be a parabola opening downward, and the vertex of this parabola will be the maximum point of the graph. Since we need to determine a value of x in which the company makes the greatest profit, we need to determine the value of x at the vertex of the parabola.

Recall that x = -b/(2a) is the formula to find the x-value of the vertex; therefore, the number of workers that maximizes the profit is:

x = -20,000/[2(-25)] = -20,000/-50 = 400

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Manager
Joined: 29 Dec 2014
Posts: 69
Re: It’s well known that a company's profit=20,000x-25x^2, where x is the [#permalink]

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12 Nov 2016, 06:52
Noted, thanks for the clarification!
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Re: It’s well known that a company's profit=20,000x-25x^2, where x is the [#permalink]

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26 Nov 2017, 17:16
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Re: It’s well known that a company's profit=20,000x-25x^2, where x is the   [#permalink] 26 Nov 2017, 17:16
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