It’s well known that a company's profit=10,000x-50x2, where x is the n

Question

It’s well known that a company's profit=10,000x-50x^2, where x is the number of workers. If the profit of the company is the greatest, what is the value of x?
 
A. 5 
B. 10 
C. 50 
D. 80 
E. 100

Spartan85 · Accepted Answer

Answer :

To find Max or Min of a polynomial f(x), Equate f'(x)=0

f(x) = 10,000x - 50x^2

f'(x) = 10,000 - 50*2x = 0

100x = 10,000

x=100

Bunuel · Answer

This is almost the same exact question as this one: https://gmatclub.com/forum/it-s-well-kn ... 27127.html

gvvsnraju@1 · Answer

value of given expression increases as no of workers.

So E

joondez · Answer

Haha this is how I solved the question too, but this is calculus. I think GMAT does not require calculus? Is this a realistic question for the test?

Spartan85 · Answer

Assuming that this type of problem may come on the GMAT, knowing only this little part of Calculus is highly recommended. :-D

MathRevolution · Answer

==> From  y=f(x)=ax^2+bx+c , if  x=\frac{-b}{2a} , f(x) becomes either maximum or minimum. Thus, profit= -50x^2+10,000x , and in order for the profit to become the greatest, you get  x=\frac{-10,000}{2(-50)}=100 .

The answer is E. 
Answer: E

mbsingh · Answer

Bunuel   MathRevolution

i got stumped by similar questions before. So when the question says 10,000x does that mean x is multiplied by 10,000 or is it the units digit ?
I know 10,000 (thousands comma separator) should give it away but other questions dont have it sometimes

and also for 50x^2 is that x squared or (50X) squared.

Thanks

Bunuel · Answer

10000x always means 10000*x. If it were an units digit it would have been explicitly mentioned.

50x^2 always means 50*x^2. If it were (50x)^2 would have been written (50x)^2.

mbsingh · Answer

Thanks  Bunuel . I wish i could borrow your brain for exam day. Not a bad trade off, mine comes with long list of pick up lines and quality stuff for stand up comedy :D

amanvermagmat · Answer

well we can do it this way also:

10000x - 50x^2 = -50 (x^2 - 10000x/50) = -50 (x^2 - 200x) (I have taken -50 outside common)

= -50   (I have written it in a square form, it is still the same)

= 50   (Now removed the minus sign outside and changed inside, so still same)

Now, if we observe, the MAX value of this expression will be when (x-100) becomes '0' (zero), and that will only happen when x=100.

So  E answer

gps5441 · Answer

It is easier to plug the value of x given in the answer choices.
Start with the max then the min and the middle. we will get our range.
X=100 
10000X100-50(100)ˆ2=(10)ˆ6-5(10)ˆ5
X=5
10000X5-50(5)ˆ2=5(10)ˆ4-1250
X=50
10000X50-50(50)ˆ2=5(10)ˆ5-125(10)ˆ4
The highest power of 10 we get when X=100

Amyy2692 · Answer

precisely how I got my answer. Coz the question asks for the “maximum” value. Sure got taken aback when I saw people using calculus.

Sent from my iPhone using  GMAT Club Forum mobile app

Paras96 · Answer

company's profit P=10,000x-50x^2

Using calculus P max when dP/dx = 0

=> dP/dx=10,000-100x=0

=>x=100 
Hence E

Therefore Pmax = P(x=100)=10,000*100-50*100*100=500,000

AnuK2222 · Answer

answer is E, 100
=10,000x-50x^2, we take 50x common
=50x(200-x).. higher the x higher value of equation (given x<200) and 100 fits this requirement
hope this is correct, thanks

Oppenheimer1945 · Answer

f(x)=10000x-50x^2

df/dx= 10000-100x=0 => x=100

bumpbot · Answer

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It’s well known that a company's profit=10,000x-50x2, where x is the n

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It’s well known that a company's profit=10,000x-50x2, where x is the n

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