Functions

gmatmachoman 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)

NOT FOR GMAT

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].

Hi, can u elaborate wat does the cross section means?

dkumar.83 wrote:Hi, can u elaborate wat does the cross section means?

excatly this was the first question that came to my mind when i read this question......lol

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....

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?

liferocks 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?

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. Thanks