The cost C per km. of electric cable is given by C = 120 /x+ 600 x, where x is the cross - section in square cms. Find the cross section for which the cost is least and also find the least cost per km.?
OA: 240 sqrt (5)
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NOT FOR GMATgmatmachoman wrote:The cost C per km. of electric cable is given by C = 120 /x+ 600 x, where x is the cross - section in square cms. Find the cross section for which the cost is least and also find the least cost per km.?
OA: 240 sqrt (5)
Kamaal ho tussi...
C' = -120/x^2 + 600
For minimum C, C' = 0
Or 120/x^2 = 600
Or x^2 = 1/5
(C'' for verification is skipped here)
Or the cross section for which the cost is least is [spoiler]1/√5[/spoiler], and hence the minimum cost
= 120 √5 + 600/√5
= 1200/√5
= [spoiler]240 √5[/spoiler].
The mind is everything. What you think you become. -Lord Buddha
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Cross section is if you were to cut the wire and hold it in front of you with the wire pointing towards you ..... you could see a circle, square etc. - refer link - https://www.google.co.in/imgres?imgurl=h ... CB4Q9QEwAA
but it does not matter what is the shape since the question states the area is "x" sq cm....
but it does not matter what is the shape since the question states the area is "x" sq cm....
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Let a=120 /x and b=600 x
then ab=120/x*600x=120*600..a constant
if ab is a constant a+b will be minimum when a=b
so when cost is minimum, a=b=sqrt(120*600) or 120*sqrt(5)
so for minimum cost 600x=120*sqrt(5) or x=1/sqrt(5)
and minimum cost is [spoiler]2*120*sqrt(5)=240*sqrt(5)[/spoiler]
@Sanju,Doesn't take much time to calculate..why do you think its not a GMAT type?
then ab=120/x*600x=120*600..a constant
if ab is a constant a+b will be minimum when a=b
so when cost is minimum, a=b=sqrt(120*600) or 120*sqrt(5)
so for minimum cost 600x=120*sqrt(5) or x=1/sqrt(5)
and minimum cost is [spoiler]2*120*sqrt(5)=240*sqrt(5)[/spoiler]
@Sanju,Doesn't take much time to calculate..why do you think its not a GMAT type?
"If you don't know where you are going, any road will get you there."
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Didn't think that way on this occasion, otherwise the Maxima and Minima concepts of calculus are not checked on GMAT, and I did it that way only, that's why the undue remark. Thanksliferocks wrote:Let a=120 /x and b=600 x
then ab=120/x*600x=120*600..a constant
if ab is a constant a+b will be minimum when a=b
so when cost is minimum, a=b=sqrt(120*600) or 120*sqrt(5)
so for minimum cost 600x=120*sqrt(5) or x=1/sqrt(5)
and minimum cost is [spoiler]2*120*sqrt(5)=240*sqrt(5)[/spoiler]
@Sanju,Doesn't take much time to calculate..why do you think its not a GMAT type?
The mind is everything. What you think you become. -Lord Buddha
Sanjeev K Saxena
Quantitative Instructor
The Princeton Review - Manya Abroad
Lucknow-226001
www.manyagroup.com
Sanjeev K Saxena
Quantitative Instructor
The Princeton Review - Manya Abroad
Lucknow-226001
www.manyagroup.com