Question

if x+y=60 and xy3 is maximum then x and y respectiyely wll be​

Answer 1

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MATHS

Find two positive numbers x and y such that x+y=60 and xy

3

is maximum.

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ANSWER

Let P=xy

3

It is given that x+y=60

⇒x=60−y

P=(60−y)y

3

[Putting value of x]

=60y

3

−y

4

⇒

dy

dP

=180y

2

−4y

3

dy

2

d

2

P

=360y−12y

2

For maximum or minimum values of y, P we have

dy

dP

=0

⇒180y

2

−4y

3

=0

⇒4y

2

(45−y)=0

⇒y=0 45−y=0 y=45

Now (

dy

2

d

2

P

)

y=45

=360×45−12(45)

2

=12×45−(30−45)

=−8100<0

P is maximum when y=45

when y=45 x+y=60 ⇒x=60−45

x=15

Numbers are 15 and 45