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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?

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

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12 Oct 2016, 02:59

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.

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

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12 Oct 2016, 10:16

1

This post received KUDOS

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

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
_________________

==>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, 02:06

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 ) So, Answer will be (E)

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.

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

Answer: E
_________________

Scott Woodbury-Stewart Founder and CEO

GMAT Quant Self-Study Course 500+ lessons 3000+ practice problems 800+ HD solutions

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, 16:16

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